Index
Aamaket, tomb of 232
Abd el-Latyf 70
Abu Rawash 193, 225, 245
Abusir 61, 181, 183, 206, 207, 230, 231, 247
Abydos 30, 180, 181, 183, 232, 234
Agrigentum, temple of the Concord at 13
Ahmose (Eighteenth Dynasty) xxi, 181, 232
Akhenaten (Amenhotep IV, Eighteenth Dynasty) xxi, 99, 129
Alberti, Leon Battista 3
Alexander the Great xxi, 172
Alexandria 68
algorithm 58
Amada 105
Amarna 47, 73, 99, 101, 105, 127, 129, 153, 155
Royal Tomb 83–84, 141
period xxi, 104
Amduat 141
Amenemhat I (Twelfth Dynasty) xxi, 203, 229, 230, 251
Amenemhat II (Twelfth Dynasty) xxi, 229, 252
Amenemhat III (Twelfth Dynasty) xxi, 104, 115, 135, 138, 174, 183, 194, 206, 230, 253–254
Amenemhat IV (Twelfth Dynasty) xxi
Amenemhat-Serer, statue of 154
Amenhotep III (Eighteenth Dynasty) xxi, 115, 135–138, 150, 174, 205, 212
Amenhotep IV (Akhenaten, Eighteenth Dynasty) xxi
Amenhotepsesi, tomb of 154
Amenmesse (Nineteenth Dynasty) 142, 144
Ameny Qemau (Thirteenth Dynasty) xxi, 230, 254
amulets 70–71
Aniba 181, 233
angle 2, 43, 71, 196–197
angle contraction 175
right angle 22, 88, 122, 157, 158
Antony 172
apothem 200, 203, 207–211
approximation 10, 15, 26, 35, 54, 60, 66, 67, 70, 87, 112, 175, 212–213, 214, 228
apron 69
arches
at St Chamas in Provence 13
of Titus in Rome 13
Archimedes 66–67, 215, 240
architectural drawings (see also drawings and geometrical drawings) xv, 10, 60, 83, 90, 101, 113, 124, 127–128, 129, 139, 140, 141, 166, 174, 240
of a building from Lisht 104
of a building from the Ramesseum 104
of a building from the Sheikh Said quarry 104, 105
of a capital from Gebel Abu Foda 113, 117–121
of a capital from the temple of Kalabsha 113
of a cavetto cornice from the temple of Edfu 113
of a colonnaded court from Dra Abu el-Naga 104
of a column from the Temple of Philae 113, 117–121, 127, 167
of a curve with coordinates from Saqqara 104, 115
of an elliptical vault from the tomb of Ramses VI 113, 114–115, 157, 158, 159, 218
of a four-pillared chamber of a tomb 104, 105–109, 144, 147
of a garden or temple from Deir el-Bahari 104
of a Hathor-headed capital from Gebel Abu Foda 113, 122, 167
of a house 104
of a house from Amarna 104
of a peripteral chapel (?) on a wooden board 104, 109–112
of a peripteral chapel from Deir el-Bahari 104, 105, 107, 111
of pyramids 14 and 15 at Soleb 104, 186
of a pyramid from Meroe 104, 186
of a shrine: see of a peripteral chapel from Deir el-Bahari
of the sloping sides of Mastaba 17 at Meidum 113, 114, 188–192
of the stairs and door of a tomb 104
of a temple at Heliopolis 100–101, 104
of a tomb, from the tomb of Senenmut 104, 105–109
of the tomb of Ramses IV 104, 112
of the tomb of Ramses IX 104, 112
vertical section of pyramid Beg. 8 at Meroe 104, 192, 234
architectural models xv, 90, 127–128, 138, 174, 175, 192, 194–195
of columns and capitals 135–138
of a granary 128
of a house 128
of the funerary apartment of a pyramid from Dahshur 128, 135–138, 175
of the pyramid of Hawara(?) 128, 135–138, 194
of a step pyramid 128, 131–133, 135, 194
of a temple of Seti I 128, 129–131
of the temple of Tôd 128, 129, 131–133
from the tomb of Meketra 128
of a T-shaped basin from Amarna 128
votive 129, 131, 133, 135, 138
architecture 2, 4, 5, 10, 61, 87, 88, 122, 240
Achaemenid 16
Egyptian xv, xvi, 5, 6, 7, 10, 16, 28, 31, 46, 57, 69, 85, 86, 87, 127, 138, 155, 162, 173, 176, 180, 182, 226, 239
Greek 7, 10, 90, 127, 173, 176
Minoan 79
relationship with mathematics xiv–xv, 2
Roman 90, 176
archive 100
area of the circle 215
Arsenal inscription 175
art 2, 4, 5, 226
Egyptian 2, 10, 31, 57, 85, 86, 96, 154–155
Greek 7, 10
Ashmunein 85
Atmu-neferu, Queen of Senusret II (Twelfth Dynasty) 212, 252
Augustus xxi, 167, 172
axis 42, 43, 71, 122, 133, 153, 166, 187, 192, 207, 211
basalt 206, 207, 230
Basilica of Constantine 11–13
Belzoni, Giovanni 239
benben stone 182, 185, 198
benbenet (see also capstone and pyramidion) 182–183, 184
Beni Hasan 4
Bent Pyramid: see pyramids
Bryson 66
Building Texts 85, 117, 159, 161–172
burial chamber of a tomb (see also ‘house of gold’ and ‘hall’) 140
Byzantine division table 121
Byzantine Period xxi
Cagliostro 239
Cairo Calendar: see Papyrus Cairo 86637
Calendars of Lucky and Unlucky Days 80–81
capital 2, 18–43
sketch from Gebel Abu Foda 113, 117–121
sketch from the temple of Kalabsha 113
sketch of a Hathor-headed from Gebel Abu Foda 113, 122, 167
capstone (see also pyramidion) 138, 182, 184, 207, 208, 211
cathedrals
Amiens 13
Notre-Dame de Paris 13
catheti 4, 28, 67, 185, 192, 203
cavetto cornice 113
cenotaph 135, 181, 232, 243, 244
chapel (see also peripteral chapels)
of Hakoris at Karnak 54, 124
of Ti 5
Chefren: see Khafra
Cheops: see Khufu
circle 5, 11, 32, 65, 66, 90, 115, 200
calculation of the area 60
Greek method 66–67
Egyptian method 65–67
circumference 65, 66–67, 115, 200, 201
Clemens of Alexandria 156–157
Cleopatra VII xxi, 172
Colonna, Francesco 239
columns 2, 15, 18–43, 96, 97, 101, 114, 127, 132–133, 226
drawing from the Temple of Philae 113, 117–121, 127, 167
cords (see also ropes) 61, 71, 115, 152, 153, 154–159, 216
‘stretching the cord’: see foundation ceremonies
corridors
of pyramids 197, 224
of tombs 84, 140, 142
slope of 141, 142, 218
Corinth, temple of 13
Concord at Agrigentum, temple of 13
Crete 79
cubit (unit of measurement) 54, 59–60, 61, 85, 88, 109, 111, 112, 115, 117, 121, 122–123, 124, 127, 129, 142–147, 154, 155, 159, 166, 167, 171, 185, 188, 191, 192, 197, 202, 208, 212, 213–214, 218, 219, 226, 228, 229, 233, 234, 236, 242–254
small cubit 59, 61, 129, 226
royal cubit 59, 61, 129, 141, 201
cubit rod 61, 88, 112, 124, 174
Dahshur 128, 135, 174, 181, 192, 207, 221, 229, 243, 252–254
deben (unit of measurement) 61
Deir el-Bahari 104, 122, 153, 155, 174
Deir el-Medina 79, 101, 139, 181, 232–233
Democritus 156–157
Dendera, temple of 31, 85, 149, 151, 153, 166, 170
deny (unit of measurement) 61
design 49, 73, 81, 90, 105, 117, 131, 142, 159, 162, 166, 176, 202, 204
diameter 66–67, 115, 127, 132, 156, 200–201, 215
Diodorus Siculus 70
division table, Byzantine 121
dja (unit of measurement) 61
Djedefra (Fourth Dynasty) xxi, 193, 225–226, 245
Djedkara-Isesi (Fifth Dynasty) xxi, 203, 226, 248
Djehuti-nefer Huia, house of 100
djeser (unit of measurement) 61
Djeserkaraseneb, tomb of 154
Djoser (Third Dynasty) xxi, 180, 181, 218, 226
Dra Abu el-Naga 104, 181, 232
‘doorkeeper’s rooms’ (elements of a tomb) 140
drawings (see also architectural and geometrical drawing) xiv, 18, 46, 47, 59, 81, 122, 157
of buildings 96–101
of a shrine on papyrus, from Gurob 2, 174
scale drawings 54, 85, 101–112, 113, 174
Dynasty 0 xxi
Early Dynastic Period xxi, 124, 152, 162
Edfu, temple of 7, 85, 113, 149, 151, 162, 163, 166–173
Egina, temple at 13
Egyptian Mathematical Leather Roll 57
Eighth Dynasty xxi, 251
Eigtheenth Dynasty xxi, 100, 101, 104, 105, 109, 122, 124, 127, 140, 149, 154, 164, 181, 197, 232, 233
Elephantine 18–22, 47, 68, 105, 163, 166
Eleventh Dynasty xxi, 104, 149
ellipse 114, 115
construction of 115–117
drawing from the temple of Luxor 113
elliptical vault in the tomb of Ramses VI 113, 114–115, 157, 158, 159, 218
Euclid 63, 65, 67, 68, 89, 240
extreme and mean ratio: see mean and extreme ratio
Ezbet Rushdi 206, 207, 211, 230, 254
&dfd; 24, 26, 28, 29, 30, 35, 54, 56, 57, 58–60, 67, 68, 78, 87, 175, 200
Fibonacci
Leonardo from Pisa 26
numbers 59, 67
series 26, 35, 42, 56, 59, 67, 68, 79, 81
Fifth Dynasty xxi, 61, 182, 203, 206, 215, 226, 230, 231, 238, 246–249
Fifteenth Dynasty (Hyksos) xxi
finger (unit of measurement) 59–60, 61, 109, 111, 112, 115, 117–121, 132–133, 141, 146, 147, 167, 185, 212, 213–214, 219–221, 224–234, 242–254
First Dynasty xxi, 148, 156, 184
First Intermediate Period xxi, 150, 167, 228
formula xvi, 2, 4, 5, 58, 63, 81, 171
fortress at Semna South 149
foot (unit of measurement) 61
foundation ceremonies 42, 57, 131, 147, 148–153, 157–158, 171
foundation deposits 149, 153, 155
‘stretching the cord’ 148, 149, 151–153, 155
four-pillared chamber of a tomb, drawing of 104, 105–109, 144, 147
Fourth Dynasty xxi, 113, 181, 192, 193, 197, 203, 206, 243–246
Fourteenth Dynasty xxi
fractions 58, 66, 67, 117–121, 167–173, 175, 212
Horus-Eye 61, 68
unit 58, 67
Freemasons 239
full-size sketches 113
Gebel Abu Foda 113, 117, 122, 167
Gebel Barkal 181, 234
geometry 2, 4, 178, 201, 202, 225, 234
geometrical drawing of an ellipse from the temple of Luxor 113
geometrical figures xiv, 5, 10, 11, 15, 35, 54, 66, 68, 69, 70, 73, 78, 80, 81, 83, 87, 156, 176, 215, 240
geometrical models 70, 204, 213, 219, 221, 226–227, 234, 236–238, 240
geometrical progression (see also numerical series) 58–59, 67
Giorgi, Francesco 3
Giza 2, 5, 181, 202, 206, 225, 226, 244, 245, 246
gnomonic expansion 26, 29
‘god’s passage’ (element of a tomb) 140
‘ . . . which is upon the sun’s path’ 140
Goethe, Johann Wolfgang 239
Golden Section 5, 10, 16, 22, 23, 28–31, 32, 35, 42, 46, 57, 60, 67–68, 78, 79, 80–85, 86, 173, 200
names of 23
psychological experiments 78–79, 80, 81, 85, 240
tendency towards 69, 73, 78–80, 83, 85, 86, 240
golden rectangle 83, 85
golden triangle 201
Graeco-Roman Period 58
granite 206
Great Aten Temple 47, 99, 101, 155
‘Great Pyramid’ (see also pyramid of Khufu) 200–202
Greece 127, 138, 239
grids: see square grids
guide-lines 28, 81, 113–114, 122
Gurna 155
Gurob 174, 233
hall 49
element of a tomb:
‘another hall of repelling rebels’ 140
‘chariot hall’ 140
‘hall of denial of access’ 140
‘hall of hindering’ 140, 141
‘hall of truth’ 140
‘hall in which one rests’ 140
handsbreath (unit of measurement) 61
harmony 2, 3, 4, 28
Harpedonaptai 157
Hawara 128, 138, 194
Hatshepsut (Eighteenth Dynasty) xxi, 122, 129, 153, 155, 183
hekat (unit of measurement) 61, 117
Heliopolis 100–101, 104, 182, 183
Hellenistic Period 127, 138, 175, 176, 240
Hemaka, tomb of 156
heptagon 42, 201
Heracleopolis xxi
Herodotus 70
heseb (unit of measurement) 61
Hetepsekhemwy (Second Dynasty) xxi, 180
hexagon 5, 11
Hierakonpolis 164–166
hinu (unit of measurement) 61
Horus-Eye fractions: see fractions
house 101, 128
drawing of 104
model of 128
‘house of gold’ 140
of Djehuti-nefer Huia 100
soul-houses 128
human body
representation of 28–29, 81–83, 96, 97–99, 122
proportions of 3, 5, 10, 28–29
Huni (Third Dynasty) 135, 181
Hyksos xxi
hypotenuse 22, 64, 67
Iby (Eighth Dynasty) xxi, 228, 251
icosahedron 68
Imhotep 10
Inenek-Inti, Queen of Pepi I (Sixth Dynasty) 249
Iput I, Queen of Teti (Sixth Dynasty) 219, 227, 228, 229, 230, 249
Iput II, Queen of Pepi II (Sixth Dynasty) 206, 228, 251
Iry, tomb of 232
Isis, Queen of time of Ramses VI (Twentieth Dynasty) 144
Islamic Period xxi
Itakajet, Queen no. 2 of Senusret I (Twelfth Dynasty) 251
el-Kab 105
Kalabsha, temple of 71–72, 101, 113, 123
Kamose (Seventeenth Dynasty) xxi, 232
Karnak 11, 31, 54, 105, 109, 123, 150, 155, 183
kha (unit of measurement) 61
Khaba (Third Dynasty) xxi, 181
khar (unit of measurement) 61
kha-ta (unit of measurement) 61
Khaemhat, tomb of 154
Khaemwaset, son of Ramses III (Twentieth Dynasty) 144
Khafra (Chefren, Fourth Dynasty) xxi, 203, 207, 219, 226–227, 236–238, 245
Khasekhemwy (Second Dynasty) 149
Khedival Period xxi
Khendjer (Thirteenth Dynasty) xxi, 183, 205, 206, 207, 208, 211, 212, 230, 254
Khentkawes, Queen of Menkaura (Fourth Dynasty) 181
Khentkawes, Queen of Neferirkara (Fifth Dynasty) 206, 207, 247
khet (rod, unit of measurement) 61, 117, 154
Khnum Hotep, tomb of 4
Khonsu, tomb of 232
Khui 228
Khuit, Queen of Teti (Sixth Dynasty) 227, 249
Khufu (Cheops, Fourth Dynasty) xxi, 13, 22, 28, 30, 31, 70, 200–201, 202, 203, 206, 207, 212, 213, 215–216, 219, 225, 226, 236–238, 244, 245, 246
Kircher, Athanasius 239
kite (unit of measurement) 61
Kom Ombo, temple of 172
Kuban 105
el-Kurru 181, 234
Lahun 206, 213, 252
land measuring 154
Late Dynastic Period xxi
Late Period xxi, 87, 104, 122, 128, 131, 159, 181, 182, 186, 213, 221, 224, 231, 234
Leonardo from Pisa, also called Fibonacci 26
limestone 128, 135, 138, 206
Lisht 104, 229, 230, 251
Lucas numbers 26
Luxor, temple at 28, 30, 113, 151
Macedonian Dynasty xxi
Macedonian Period xxi
Mammisi at Dendera 167
Martini, Francesco di Giorgio 28
mastaba 180, 181, 184, 192, 228, 249
17 at Meidum 113, 114, 188–192
of Ptahshepses 61
Mastabat el-Faraƈun 113
mathematics 2, 4, 87, 89, 90, 117, 179, 200, 226
Babylonian 64
Egyptian 71, 87, 90, 202
Greek 66, 67
relationship with architecture xiv–xv, 179
mathematical sources 57, 67, 68, 71, 90, 178, 203, 217, 218, 240
Berlin Papyrus 217
Egyptian Mathematical Leather Roll 57
Kahun Papyri 57, 218
Moscow Mathematical Papyrus 57, 154, 218
Rhind Mathematical Papyrus (RMP) 57, 65, 154, 185, 218, 240
Mazghuna 254
mean and extreme ratio (see also Golden Section) 5, 22, 23, 67, 68
Medinet Habu 150
Meidum 113, 114, 184, 188, 192, 203, 212, 215–216, 221, 225, 226, 236–238, 244, 246
Meketra, models from the tomb of 128
Memphis 128, 133
Menkauhor (Fifth Dynasty) xxi, 248
Menkaura (Mycerinus, Fourth Dynasty) xxi, 113, 133, 181, 193, 206, 207, 226, 246
Menna, tomb of 154
Mentuhotep II Nebhepetra (Eleventh Dynasty) xxi, 104
Merenptah (Nineteenth Dynasty) xxi, 144
Merenra I (Sixth Dynasty) xxi, 203, 227, 250
Meritites, Queen of Pepi I (Sixth Dynasty) 250
Merneferra Ay (Thirteenth Dynasty) xxi, 183, 206, 211, 230, 254
Meroe 104, 181, 234
monuments 56, 173, 234
pyramids 178, 182, 192, 194, 197, 234
temples 127
Middle Kingdom xxi, 47, 57, 58, 68, 70, 80, 104, 117, 122, 124, 138, 149, 156, 205, 208, 211, 217, 218, 221, 224, 228, 231, 234, 236, 238, 240
model (see also architectural and geometrical models) 226, 229, 240
module 23, 47, 71, 121–127
Mycerinus: see Menkaura
Nakht Min, tomb of 232
Napata xxi
Nebka (Fourth Dynasty?) xxi, 246
Nebnefer, tomb of 233
neby (unit of measurement) 61, 141
Nectanebo I (Thirtieth Dynasty) xxi, 85, 167
Nectanebo II (Thirtieth Dynasty) xxi, 172
Neferhetepes, Queen of Userkaf (Fifth Dynasty) 246
Neferirkara (Fifth Dynasty) xxi, 181, 203, 226, 247
Neferuptah, Queen or daughter of Amenemhat III (Twelfth Dynasty) 138, 254
Neith, Queen of Pepi II (Sixth Dynasty) 228, 250
Neuserra (Sixth Dynasty) xxi, 113, 149, 181, 184, 203, 206, 215, 247
New Kingdom xxi, 61, 88, 101, 104, 129, 131, 150, 153, 155, 158, 163, 172, 178, 180, 186, 213, 221, 224, 231, 234, 235, 240
Ninetjer (Second Dynasty) xxi, 180
Ninth Dynasty xxi
Nineteenth Dynasty xxi, 104, 112, 128, 144, 181, 197, 202, 233
Nofru, Queen no. 1 of Senusret I (Twelfth Dynasty) 219, 229, 230, 238, 251
Nubwenet, Queen of Pepi I (Sixth Dynasty) 249
number 2, 3, 60–63, 65, 68, 88, 166, 171, 187–188, 200
integers (whole) 58, 60, 216, 218
irrational 4, 24, 54, 68, 202
numerical series (see also geometrical progression) 59, 167
numerologists 167, 201–202
Nubia 181, 233
Nuri 181, 234
obelisks 129, 131, 149, 156, 182–183, 184, 215
octagon 65, 66
Old Kingdom xvi, xxi, 2, 5, 64, 65, 71, 81, 87, 117, 122, 124, 149, 150, 156, 158, 159, 164, 178–179, 180, 192, 197, 204, 205, 207, 218, 221, 224, 226, 231, 234, 235, 236, 238, 240
orders
Doric 175–176
Ionic 175–176
Osireion 30
ostraca
Cairo 25184 104, 142–146
Cairo 25536 recto 140, 144
Cairo 25537 140, 144
Cairo 25538 140, 144
Cairo 25581 recto 140, 144
Cairo 50036 104
Cairo 51936 104, 144, 147
Cairo 66262 104
Cairo 72452 140
Cairo (number not known) 144
Berlin B 144
BM 8505 140, 144
BM 41228 104
BM 65944 (Nash 10) 144
DeM (number not known) 144
Gardiner 109 80
mathematical from Elephantine 68
Michaelides 53 144
Michaelides 71 140
Michaelides 92 144
Strasburg H.112 139, 142, 144
Turin 57036 140, 144
Turin 57037 140, 144
Ottoman Period xxi
Palermo Stone 117, 149
Palladio 3
palm (unit of measurement) 59–60, 61, 88, 109, 112, 115, 117–121, 129, 132–133, 141, 146, 147, 167, 174, 185, 192, 203, 208, 212, 213–215, 219–234, 242–254
paradeigmata 138
Parthenon 13
papyri 101, 226
Berlin 6619 217
Budge 80
Cairo 86637 verso 80, 144
Demotic mathematical 58, 64, 217
Kahun 57, 218
Moscow Mathematical 57, 154, 218
Ram. B 104
Reisner 117, 218
Rhind Mathematical 57, 65, 154, 185, 218, 240
Sallier IV 80
Turin 1885 recto 144, 147
Turin 1885 verso 104, 144
Turin 1923 142, 144
Penanhor, statue of 154
Pepi I (Sixth Dynasty) xxi, 159, 203, 227, 238, 249–250
Pepi II (Sixth Dynasty) xxi, 159, 183, 203, 206, 227, 228, 238, 250–251
perimeter 66, 90, 167, 200–203, 204, 228
peripteral
chapels 105
chapel(?) on a canal, drawing of 104, 109–112
chapel from Deir el-Bahari, drawing of 104, 105, 107, 111
temple at Elephantine 47
temple of Tuthmosis III at Karnak 109–111
Persian Period, first and second xxi, 172
Petosiris, tomb of 28, 85
Philae 113, 117, 127
phoenix 182
&dfdf; 28, 60, 65, 67, 87, 175, 200, 202
Piranesi, Giovan Battista 239
plan (architectural) xiv, 10, 42, 43, 47, 54, 60, 71, 73, 83–84, 87, 90, 97, 100–101, 105–112, 122, 124, 127–128, 131–133, 138, 139, 141, 142–146, 147, 153, 155, 156, 158, 159, 167, 176, 186, 207, 216, 226, 240
Plato 2–3, 64, 88
Platonic philosophy 3
Platonic influence 64
Plimpton 322 64
Plutarch 64, 240
polygon 65, 66
Predynastic Period 43, 156, 162, 164
project 69, 70, 87, 90, 101, 109, 122, 135, 138, 140, 141, 142, 147, 166, 174, 175, 197, 206, 207, 221, 224
proportions xiv, 4, 11, 22, 70, 72, 112, 113, 117, 122, 129, 132, 159
in architecture xiv, xv, xvi, 3, 6, 7, 16, 42, 47, 57, 69, 83, 85, 90, 101, 129, 131, 156, 171, 176, 194, 195, 203, 204, 205, 211, 212–213, 216, 219, 221, 226–227, 229, 232, 233, 236, 238, 239
mathematical 5, 23, 24, 28, 29, 67, 68, 78, 79, 81, 85, 86, 219
canon of 10
of the human body 3, 5, 10, 28–29
Ptahshepses, mastaba of 61
Ptolemaic Dynasty xxi, 172
Ptolemaic Period xxi, 43, 113, 117, 138, 148, 150, 162–173, 236
Ptolemaic temples: see temples
Ptolemy xxi, 172
Ptolemy II xxi, 172
Ptolemy III xxi, 166, 171
Ptolemy VI Philometor xxi, 117, 167, 172
Ptolemy VIII Euergetes II xxi, 166, 172
Ptolemy X xxi, 167
Ptolemy XI xxi, 167
Ptolemy XII Auletes xxi, 166, 171
pylon 4, 101, 129, 131, 163
pyramidia (see also capstones) 138, 182–184, 186, 195, 205–211, 212, 231
of Aamaket 232
of Amenemhet III 183, 205, 206, 208, 211, 253
from Dahshur 206, 207, 243
from Ezbet Rushdi 206, 207, 230
from Gurob 233
of Iput II 206
of Iry 232
of Khendjer 183, 205, 206, 207, 208, 211, 230, 254
of Khentkawes II, Queen of Neferirkara 206, 207, 247
of Khonsu 232
Late Period from Abydos 183, 197, 234
of Merneferra Ay 183, 206, 211, 230, 254
New Kingdom 183, 197, 233
of Qaha 232
of Queen GIIIa of Menkaura 206, 207, 246
of a Queen of Neuserra (Lepsius 24 and 25) 206, 207, 230, 231, 248
of the satellite of Khufu 206, 244
of Sahura 183
of Sekhemra-Wepmaat Intef V 232
of Sennedjem 232
of Senusret II 183, 206
of the sun temples 184, 215
of Tia and Tia 233
truncated, from South Saqqara 206, 209–211, 230, 254
of Turbay 232
of Udjebten(?) 228, 250
unfinished, from South Saqqara 206, 209–211, 230, 254
Pyramid Texts 4, 182, 184
pyramidologists 202
pyramids 4, 22, 64, 69, 70, 71, 83–138, 176, 180, 182, 184–185, 228, 231, 240
‘primeval’ 11–13, 15, 70
queens’ 205, 236, 238
satellite 133, 181, 197, 199, 203, 205, 206, 207, 212, 225, 227, 228, 229, 236, 238, 243, 244, 245, 246, 247, 248, 249, 250, 251
step 133, 135, 180–181, 193, 216, 226, 234, 244, 247
model of 128, 131–133, 135, 194
shape of steps 133
‘Buried Pyramid’ 181
of Djoser at Saqqara 115, 133, 180, 184, 216, 218
of Khaba 181
‘Layer Pyramid’ 133, 181
at Meidum 133, 135, 181, 184, 186, 192, 197–199, 216, 225
no. 29 at Saqqara 135
of Sekhemkhet 133
satellite of Meidum 133
at Sinki 133–135
small, dating to the reign of Huni 135, 181
unfinished at Zawiyet el-Aryan 135
true 69, 135, 181, 184, 213, 221, 226, 242–254
base of 70, 178, 185, 192, 200–201, 203, 204, 207–211, 216, 219, 224, 225, 242–254
drawings of: see architectural drawings
casing of 133–135, 192–193, 197, 198, 203, 205, 212, 215, 216, 221, 225, 245, 247, 251, 252–254
corner of 70, 186, 200, 203, 204, 208
diagonal of 70, 187–188, 192, 204, 207
face of 70, 178, 186, 188, 207–211, 215
height of 70, 178, 185, 200–201, 202, 203, 204, 216, 219, 224, 242–254
models of: see architectural models
slope of (see also seked) 23, 69, 70, 90, 135, 178, 185, 188–193, 196, 197–199, 202–204, 205–211, 212, 221, 226, 228, 236, 238, 242–254
vertical section of 69, 70, 185, 192, 194, 195, 201, 207–208, 214, 215, 219, 221, 234
of Ahmose
at Dra Abu el-Naga 181, 232
at Abydos 181, 232
of Amenemhat I 203, 229, 230, 251
of Amenemhat II 229, 252
of Amenemhat III
at Dahshur 115, 174, 205, 212, 230, 253–254
at Hawara 135–138, 230, 254
of Ameny Qemau 230, 254
at Aniba 233
of Atmu-neferu, Queen of Senusret II 212, 252
Beg. 8 at Meroe 192, 234
Bent Pyramid 69, 70, 181, 192, 193, 203, 206, 207, 212, 215, 221–225, 243, 251
of Djedefra 193, 225–226, 245
of Djedkara-Isesi 248
at Gebel Barkal 181, 234
GIa, of a Queen of Khufu 212, 244
GIb, of a Queen of Khufu 212, 244
GIc, of a Queen of Khufu 212, 244
GIIIa, of a Queen of Menkaura 246
GIIIb, of a Queen of Menkaura 133, 181, 246
GIIIc, of a Queen of Menkaura 133, 181, 246
of Iby 228, 251
of Inenek-Inti, Queen of Pepi I 249
of Iput I, Queen of Teti 227, 228, 229, 230, 249
of Iput II, Queen of Pepi II 228, 251
of Itakajet, Queen n. 2 of Senusret I 251
of Kamose 232
of Khafra 203, 207, 219, 226–227, 245
of Khendjer 205, 212, 230, 254
of Khentkawes II, Queen of Neferirkara 247
of Khufu 13, 22, 28, 30, 31, 70, 200–201, 202, 203, 212, 213, 215–216, 225, 226, 244, 245, 246
of Khuit, Queen of Teti 71–72, 249
at el-Kurru 181, 234
Late Period 213, 221, 231, 234
Lepsius 24 and 25 (of the Queens of Neuserra?) 183, 206, 207, 228, 231, 248
Lepsius 29 (of Menkauhor?) 248
at Meidum 203, 212, 215–216, 221, 225, 226, 236–238, 244, 245, 246
of Menkaura 113, 193, 226, 246
of Merenra 203, 227, 250
of Meritites, Queen of Pepi I 250
of Merneferra Ay 211, 230, 254
Meroitic 178, 182, 192, 194, 197, 234
Middle Kingdom xvi, 70, 178–179, 180, 204, 205, 221, 226, 231, 234, 236, 240
of Nebka 246
of Neferhetepes, Queen of Userkaf 246
of Neferirkara 181, 203, 226, 247
of Neferuptah, Queen of Amenemhat III 138, 254
of Neith, Queen of Pepi II 228, 250
of Neuserra 113, 203, 247
New Kingdom 178, 213, 221, 231, 234, 235
of Nofru, Queen no. 1 of Senusret I 219, 229, 230, 238, 251
of Nubwenet, Queen of Pepi I 249
at Nuri 181, 234
Old Kingdom xvi, 71, 178–179, 180, 204, 205, 221, 226, 231, 234, 235, 236
of Pepi I 159, 203, 227, 238, 249–250
of Pepi II 159, 203, 227, 238, 250–251
of the Queen of Djedkara 226, 248
of the Queen of Khendjer 254
of a Queen of Pepi I 250
of the Queens nos. 3, 4, 5, 6, 7, 8 and 9 of Senusret I 229, 238, 251–252
of the Queens nos. 1, 2, 3, 4, 5, 6, 7, 8 and 9 of Senusret III 229–230, 238, 252–253
of Raneferef (Lepsius 26) 247
Red Pyramid 181, 192, 199, 203, 206, 207, 219, 224–225, 229, 243
Roman 234–235
of Sahura 203, 226, 230, 247
of Sekhemra-Wepmaat Intef V 232
of Senusret I 79, 229–230, 251–252
of Senusret II 213, 252
of Senusret III 207, 212, 229, 252–253
of Shepseskara 247
of Snefru: see Meidum, Bent Pyramid and Red Pyramid
at Soleb 234
of Teti 154, 159, 203, 227, 249
of Udjebten, Queen of Pepi II 207, 228, 250
of Unas 212, 249
of unknown owner at North Mazghuna 254
of unknown owner at South Mazghuna 254
of unknown owner at South Saqqara 209, 230, 254
of Userkaf 203, 226, 246
14 and 15 at Soleb 104, 186
Pythagoras 2, 60, 89
Theorem of 60, 63–64, 65, 67, 216–217, 218
Pythagoreans 2, 28, 60
Pythagorean philosophy 3
Pythagorean Triplets 60–65, 117, 157, 216–221
3-4-5: see 3-4-5 triangle
5-12-13 221, 232, 233, 234
7-24-25 221, 232, 233, 234
8-15-17 221, 229, 230, 249, 251, 253
20-21-29 219, 224–225, 230
Qaha, tomb of 232
Qasr el-Sagha 124, 159, 226
quarry
at Gebel Abu Foda 113, 117, 122, 167
at Sheikh Said 105
quartzite 128, 129
Queen of Djedefra (Fourth Dynasty) 245
Queen of Djedkara (Fifth Dynasty) 226, 248
Queen of Khendjer (Thirteenth Dynasty) 254
Queens of Khufu (Fourth Dynasty)
buried in GIa 212, 244
buried in GIb 212, 244
buried in GIc 212, 244
Queens of Menkaura (Fourth Dynasty)
buried in GIIIa 206, 246
buried in GIIIb 133, 181, 246
buried in GIIIc 133, 181, 246
Queens of Neuserra (Fifth Dynasty) 183, 206, 207, 228, 230, 231, 248
Queen of Pepi I (Sixth Dynasty) 250
Queens nos. 3, 4, 5, 6, 7, 8 and 9 of Senusret I (Twelfth Dynasty) 229, 238, 251–252
Queens nos. 1, 2, 3, 4, 5, 6, 7, 8 and 9 of Senusret III (Twelfth Dynasty) 229–230, 238, 252–253
radius 66, 115, 121, 200, 202
Ramesseum 101, 104
Ramses II (Nineteenth Dynasty) xxi, 129, 140, 144, 151, 181, 233
Ramses III (Twentieth Dynasty) xxi, 142, 144
Ramses IV (Twentieth Dynasty) xxi, 112, 144, 147
Ramses V (Twentieth Dynasty) xxi, 142, 144
Ramses VI (Twentieth Dynasty) xxi, 113, 114, 115, 142, 144, 157
Ramses IX (Twentieth Dynasty) xxi, 112, 140, 141, 142–146
Ramsesnakht, tomb of 104
Raneferef (Fifth Dynasty) xxi, 247
ratio
1:2 124
2:3 90
3:5 90
5:4 112, 200–201
8:5 200, 234
rectangle 5, 35, 54, 69, 78, 79, 81, 85, 88, 240
Red Pyramid: see pyramids
remen (unit of measurement) 61, 88, 192
Renaissance 2–3
‘resting place of the gods’ (element of a tomb) 140
Rhind Mathematical Papyrus (RMP) 57, 65
river-measure (unit of measurement) 61
ro (unit of measurement) 61
Roman Period xxi, 113
Rome 129, 172, 234
rope (see also cord) 115, 117, 154, 155–156, 158
Rosacrucians 239
sa (unit of measurement) 61
‘sanctuaries in which the gods of the west/east repose’ (elements of a tomb) 140
sandstone 104
Sahura (Fifth Dynasty) xxi, 183, 203, 212, 226, 230, 236, 247
Saqqara 104, 115, 133, 180, 181, 184, 203, 206, 209, 218, 226, 233, 246, 248–251, 254
scale 83, 127, 129–131, 132, 135, 138, 141
drawings 54, 85, 101–112, 113, 174
Schinkel, Friedrick 239
Second Dynasty xxi, 180
Second Intermediate Period xxi, 57
secret xv, xvi, 4, 241
knowledge 87–88
seked (slope) 185–186, 192–196, 203–204, 208, 213, 236
Sekhemkhet (Third Dynasty) xxi, 181
Sekhemra-Wepmaat Intef V 232
Semna South, fortress at 149
Senenmut
statue of 154–155
tomb of 104, 105
Sennedjem, tomb of 232
Sennefer, tomb of 124
Senusret I (Twelfth Dynasty) xxi, 79, 104, 105, 149, 183, 203, 219, 229–230, 238, 251–252
Senusret II (Twelfth Dynasty) xxi, 183, 206, 213, 229, 252
Senusret III (Twelfth Dynasty) xxi, 207, 212, 229–230, 238, 252–253
Serlio 3
Seshat 42, 57, 148, 149, 153
setat (unit of measurement) 61, 88, 117, 154
Sethnakht (Twentieth Dynasty) xxi, 142
Seti I (Nineteenth Dynasty) xxi, 30, 129–131, 181
Seti II (Nineteenth Dynasty) xxi, 144, 147
Seventh Dynasty xxi, 181
Seventeenth Dynasty xxi, 231
Shabaka (Twenty-fifth Dynasty) 2, 4
shaft (element of a tomb, see also well) 140, 141
shenaty (unit of measurement) 61
Shepseskaf (Fourth Dynasty) xxi, 181
Shepseskara (Fifth Dynasty) xxi, 247
shrine 131
box, sketch on ostracon 112–113
drawing on papyrus from Gurob 2, 174
drawing on an ostracon from Deir el-Bahari 104, 105, 107, 111
Siptah xxi, 144, 147
Sixth Dynasty xxi, 159, 203, 219, 226, 238, 249–250
Sixteenth Dynasty xxi
sketch: see architectural drawings
slate 100, 104
slope
of corridors of tombs 141
of corridors of pyramids 218
of tombs 141, 142
Small Aten Temple 73, 99
Snefru (Fourth Dynasty) xxi, 69, 149, 181, 184, 192, 197, 199, 203, 206, 221, 225, 226, 228, 236, 243–244
Socrates 88
solar cult 182–184
Soleb 104, 181, 186–187, 234
Spira, Fortunio 3
spiral 26
square 35, 42, 47, 49, 65, 66, 69, 70, 78, 79, 81, 85, 88–89, 90, 158, 200, 215
square grids 5, 69, 71, 81–83, 122–127, 140, 174
square root 88, 89
statuary
Greek 7
Egyptian 7
stelae 2, 5, 182
step pyramids: see pyramids
Strabo 70
Sudan 127, 173
sun temples: see temples
survey xiv, 10, 109, 132, 139, 147, 176
symbolism 65, 180, 184, 239, 240
symmetry 5, 78
axis of 42
ta (unit of measurement) 61
Tawosret xxi, 140
Tell el-Yahudiya 128, 129
temples 4, 90
at Corinth 13
of the Concord at Agrigentum 13
at Dendera 31, 85, 149, 151, 153, 166, 170
at Edfu 85, 113, 149, 151, 162, 163, 166–173
at Egina 13
Egyptian 16, 28
funerary temples of Teti, Pepi I and Pepi II 159, 219
Great Aten Temple 47, 99, 101, 155
Greek 13, 15, 127, 175
of Hatshepsut at Deir el-Bahari 122, 153
at Heliopolis 100–101
at Hierakonpolis 164, 166
of Horus at Aniba 155
at Kalabsha 71–72, 113, 123, 172
at Karnak 11, 31, 54, 105, 109, 123, 150, 155, 183
of Khons at Karnak 4, 11
at Kom Ombo 172
at Luxor 28, 30, 113, 151
Mammisi at Dendera 167
at Medinet Habu 150
of Mentuhotep at Deir el-Bahari 174
Meroitic 127
of Nectanebo I at Ashmunein 85
New Kingdom 101, 129
Osireion 30
Parthenon 13
peripteral at Elephantine 18, 47
peripteral of Tuthmosis III at Karnak 109–111
at Philae 117, 127, 151, 167, 172
primeval 161–162, 166
Ptolemaic 7, 71–72, 85, 127, 129, 151, 159, 162–173, 176, 226–227
at Qasr el-Sagha 124, 159, 226
Ramesseum 101
rock-cut 141
of Satet at Elephantine 163–164, 166
of Seti I at Heliopolis 149
Small Aten Temple 73, 99
sun temples 182, 184
of Neuserra 149
of Userkaf 215
at Tôd 47, 129, 131–133, 135, 149
valley temple of Amenemhat III at Dahshur 135
Tenth Dynasty xxi
Teti (Sixth Dynasty) xxi, 154, 159, 203, 219, 226–227, 229, 230, 249
theatre
Greek 90
Roman 90
Thebes xxi, 4, 104, 109
Themistius 66
Theorem of Pythagoras: see Pythagoras
Third Dynasty xxi, 104, 113, 115, 180, 181, 192, 193, 205, 216
Third Intermediate Period xxi, 172
Thirteenth Dynasty xxi, 205, 206, 207, 209, 211, 230–231, 254
Thirtieth Dynasty xxi, 85, 234
Ti, chapel of 5
Tia and Tia, tomb of 233
Titian 3
Tôd
model of the temple of 128, 129, 131–133
temple at 47, 129, 131–133, 135
tombs 90, 135, 155
rock-cut 69, 83–175
royal 83, 109, 139–147, 153, 174
of Aamaket at Deir el-Medina 232
of Amenhotepsesi 154
of Amenmesse (KV 10) 142
of Djeserkaraseneb 154
of Hemaka 156
of Iry at Deir el-Medina 232
K94.1 at Dra Abu el-Naga 232–233
of Khaemhat 154
of Khaemwaset, son of Ramses III (QV 44) 144
of Khnum Hotep at Beni Hasan 4
of Khonsu at Deir el-Medina 232
KV 55 141
of Meketra 128
of Menna 154
of Nakht Min at Deir el-Medina 232
of Nebnefer at Deir el-Medina 233
New Kingdom 181
Old Kingdom 122
of Petosiris 28, 85
of Qaha at Deir el-Medina 232
of Queen Isis, time of Ramses VI (QV 51) 144
of Ramses III (KV 11) 142
of Ramses IV (KV 2) 112, 144, 147
of Ramses V–VI (KV 9) 113, 114, 115, 142, 144, 157
of Ramses IX (KV 6) 112, 141, 142–146
of Ramsesnakht at Dra Abu el-Naga 104
Royal Tomb of Amarna 83–84, 141
of Senenmut, no. 71 at Thebes 104
of Sennedjem at Deir el-Medina 232
of Sennefer 124
of Sethnakht (KV 11) 142
of Seti I (KV 17) 181
of Seti II (KV 15) 147
of Siptah (KV 47) 147
of the sons of Ramses II (KV 5) 181
of the sons of Ramses III 144
of Tia and Tia at Saqqara 233
of Tawosret 140
of Turbay at Deir el-Medina 232
of Tutankhamun (KV 62) 181
no. 1138 at Deir el-Medina 233
no. 1225 at Deir el-Medina 233
no. 1301 and 1302 at Deir el-Medina 233
‘treasuries’ (elements of a tomb) 140
triangles 5, 10, 11–15, 16, 18, 23, 35, 42, 47, 49, 54, 67, 69–72, 85, 88, 171, 207, 242–254
with base equal to height (b=h) 208, 214–215, 226–227, 228, 230, 233, 248, 249–250, 251–252, 253
‘Egyptian’ 10, 11, 22, 23, 70
equilateral 10, 11, 13, 22, 23, 69, 70–72, 90, 154, 208, 214–215, 221, 225, 228, 234, 243, 245, 253
isosceles 10, 35, 42, 71, 245, 248, 250
right-angled 4, 10, 28, 35, 60–63, 66, 71, 115, 117, 159, 185, 192, 193–194, 195–196, 203–204, 213, 214, 215, 216, 218, 219, 221, 236
similar 158
1:2 35, 42, 47, 54
1:4 35, 42, 47, 54, 186
1:8 35, 42, 54
3-4-5 10–22, 23, 35, 47, 54, 60, 64–65, 70, 71, 115–117, 154, 157, 158–159, 217–218, 219, 245, 246, 247, 249, 250
8:5 10, 11, 23, 35, 42, 43, 47, 54, 56, 70–71, 72, 78, 154, 225, 234
14:11 215
Turbay, tomb of 232
Tutankhamun xxi, 181
Tuthmosis I (Eighteenth Dynasty) xxi, 183
Tuthmosis III (Eighteenth Dynasty) xxi, 4, 109, 129, 150, 155
Twelfth Dynasty xxi, 104, 128, 135, 203, 206, 231, 251–254
Twentieth Dynasty xxi, 104, 105, 112, 113, 114, 115, 144, 158, 159, 181, 218
Twenty-eight Dynasty xxi, 144
Twenty-fifth Dynasty xxi, 2, 81, 234
Twenty-first Dynasty xxi
Twenty-fourth Dynasty (Saite) xxi
Twenty-ninth Dynasty xxi, 54
Twenty-second Dynasty xxi
Twenty-seventh Dynasty xxi
Twenty-sixth Dynasty xxi, 181
Twenty-third Dynasty xxi
Udjebten, Queen of Pepi II (Sixth Dynasty) 183, 207, 228, 250
Unas (Fifth Dynasty) xxi, 212, 249
unit fractions: see fractions
units of measurement 59–60, 61, 66, 88, 124, 129, 132, 141, 154, 155, 201, 234
Userkaf (Fifth Dynasty) xxi, 203, 215, 226, 236, 246
Valley of the Kings 104, 105, 113, 114, 139, 140, 142, 153
Valley of the Queens 139, 140
vertical section of pyramids: see architectural drawings and pyramids
Vitruvius 28, 70, 88, 89, 90, 175–176
well (element of a tomb, see also shaft) 141
Window of Appearance 99
wooden boards, documents on 104, 109
Workmen’s Village at Deir el-Medina 129
Zawiyet el-Aryan 133, 135, 181, 246
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