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38647 results in Cambridge Textbooks

Page 1311 of 1933

  • 2 - Engineering Materials

  • Ajeet Singh
  • Book:
    Fundamentals of Machine Design
    Published online:
    17 July 2025
    Print publication:
    29 May 2017, pp 20-54

  • Summary

    Introduction

    An engineer has to select a suitable material for a machine element to withstand the loads coming on it. A wrong selection may lead to its failure. It has to withstand not only the load, but should possess qualities depending upon many factors like toughness, hardness, life, stiffness, etc. There is a wide range of materials now available, from which a design engineer has to choose according to the requirement of a particular component that performs a specific function.

    Material Properties

    The selection of material depends upon strength requirement, permissible deflections, mass, life, type of service, working environment, reliability, cost, quantity required, availability, and material properties. The various material properties to be considered are tabulated alphabetically in Table 2.1. Table 2.2 gives physical properties of commonly used metals.

    Classification of Engineering Materials

    Engineering materials are broadly classified as metals and non metals. Metals are of two types: Ferrous and Non-ferrous

    Amongst ferrous metals, wrought iron (WI) is the purest form of iron (Fe). A little percentage of carbon (C) increases its hardness. Steel up to 0.25 per cent carbon is called low carbon steel. Mild steel is the most commonly used and has carbon between 0.25–0.8 per cent. Items, like tools, etc., are made of high carbon steel with carbon between 0.8–1.5 per cent.

    Metals having 2–3 per cent of carbon are called cast iron and those containing carbon between 3–4 per cent are called grey cast iron. Some alloying elements like copper (Cu), chromium (Cr), lead (Pb), magnesium (Mg), manganese (Mn), molybdenum (Mo), nickel (Ni), phosphorus (P), silicon (Si), and sulphur (S) are added to improve the properties of steels and such steels are called alloy steels.

  • 9 - Stress Concentration

  • Ajeet Singh
  • Book:
    Fundamentals of Machine Design
    Published online:
    17 July 2025
    Print publication:
    29 May 2017, pp 255-285

  • Summary

    Introduction

    In the stress analysis described in the previous chapters, it is presumed that cross-sectional area remains constant and has no discontinuities like holes, etc. In actual parts, it may not be possible to have an area of cross section, which always remains constant. Hence, in these areas, where there is change in cross section, stress concentration takes place. Stress concentration can be defined as increase in stress at the areas of changing cross section and other parameters.

    Stress concentration can be due to many reasons: Variation in properties of material from point-to-point, which could be due to non metallic inclusions, blow holes in castings, or cracks or flaws in material. Local bearing pressures between two mating parts, for example, mating gear teeth, ball and races of a rolling bearing, etc. Change in cross section is the most important factor. The areas where there is change in cross section are: a step in diameter, change of cross section either with a fillet or with taper, a hole, a notch, threads, gear teeth, etc.

    Stress Concentration Areas

    Following are some examples in which change in area causes stress concentration:

    • Abrupt change in cross section Area changes abruptly at one section as shown in Figure 9.1(a). This causes severe stress concentration.

    • Change of cross section with a fillet A small radius called fillet is given to avoid sharp corners as shown in Figure 9.1(b). Stress concentration is there, but not as severe as in the case of sharp corners.

    • Gradual change in cross section Figure 9.1(c) shows gradual change in area. Stress concentration is lesser, even than that of the stress with a fillet.

  • Introduction

  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp vii-xxviii

  • Summary

    Cicero's On the Commonwealth (De re publica) and On the Laws (De legibus) represent the most significant surviving contribution to political thought in the 700+ years between the death of Aristotle and Augustine's City of God. They are ambitious and complex works, difficult to interpret not merely because so little survives of the Hellenistic philosophy on which Cicero drew, but also because we possess only parts of them: On the Commonwealth is fragmentary, and perhaps a third of it is still extant, while On the Laws not only survives only in part (three books out of at least five), but was apparently left unfinished at Cicero's death. The goal of this Introduction is to offer some background for reading these texts and some explanation of their form, structure, and arguments.

    Cicero's Public Career

    Early in December 63 BCE, the consul Marcus Tullius Cicero, having unmasked the conspiracy of Catiline and supervised the execution of several of the leading conspirators, was hailed as Father of his Country and escorted home by a crowd of grateful Romans from all ranks of society; a public thanksgiving was decreed in his honor, the first such award ever made for non-military service to the state. That moment was the summit of a remarkable career: not only had Cicero's consulate been distinguished by signal success and acclaim, but the very fact that he had achieved that office – the chief magistracy in republican Rome – and had done so at the earliest legal age of forty-two was itself unusual. Cicero was born in 106 BCE in the town of Arpinum, some 115 km southeast of Rome. The town had had Roman citizenship since 188, and Cicero's family were among its leading citizens; however, not one of them had ever held public office at Rome. Cicero's family did have strong connections among the Roman aristocracy, though, and he came to Rome very early (before the age of fifteen) to learn the ways of politics and law under the guidance of the leading orator (Lucius Licinius Crassus) and jurists (Quintus Mucius Scaevola the Augur and his cousin Quintus Mucius Scaevola the Pontifex) of the 90s and 80s. Cicero began his career as an advocate at the end of Sulla's dictatorship, and he first held public office as quaestor in 75.

  • Book 3

  • from On the Commonwealth
  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 59-78

  • Summary

    Augustine, City of God 2.21: The discussion of this topic was put off to the next day, when it was the subject of a heated debate in Book 3. Philus himself presented the argument of those who believe that the conduct of public affairs is impossible without injustice, making a strong plea not to be taken to believe this himself. He argued conscientiously on behalf of injustice against justice as if he were trying to prove, by plausible arguments and examples, that the former is useful to the state, while the latter is useless. Then Laelius at the request of everyone took up the defense of justice and asserted as strongly as he could that nothing is so dangerous to a state as injustice and that in fact a state cannot exist or be maintained without a high degree of justice.

    When this subject had been discussed to everyone's satisfaction, Scipio returned to the previous topic; he recalled and commended his brief definition of the commonwealth, in which he had said that it was the concern of the people, and that the people was not any large assemblage, but an assemblage associated with one another by agreement on law and community of interest. He then showed how useful definitions are in argument, and from these definitions of his he drew the conclusion that a commonwealth (that is the concern of the people) then truly exists, when its affairs are conducted well and justly, whether by a single king, or by a few aristocrats, or by the people as a whole. But when there is an unjust king (whom in the manner of the Greeks he called a tyrant), or unjust aristocrats (whose conspiracy he called a faction), or when the people itself is unjust – and here he was not able to find any familiar name other than to call the people itself a tyrant – then there is not a flawed commonwealth, as had been argued on the previous day, but (the logical conclusion from his definitions) no commonwealth at all: there is no “concern of the people” when a tyrant or a faction has seized hold of it, nor is the people itself still a people if it is unjust, because it is no longer a multitude associated with one another by agreement on law and community of interest, as the people had been defined.

  • Book 3

  • from On the Laws
  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 159-177

  • Summary

    MARCUS: Then I'll continue to follow that divine man; I may praise him more often than I need to because of the admiration for him which moves me.

    ATTICUS: You mean Plato, I suppose.

    MARCUS: He's the one, Atticus.

    ATTICUS: You could never praise him too much or too often. Even my own people, who never want anyone except their own founder to be praised, permit me to esteem him at my own discretion.

    MARCUS: A good decision on their part. What could be more worthy of your own refinement? Your life and language appear to me to have achieved a combination of seriousness and humaneness, something that's extremely difficult.

    ATTICUS: I'm very glad to have interrupted you, since you've given me such a grand statement of your opinion. But go on.

    MARCUS: Then shall we start by praising the law in accordance with the true praise appropriate to its kind?

    ATTICUS: Yes, just as you did with the religious law.

    MARCUS: You see, then, that this is the power of the magistrate, that he be in charge and ordain behavior that is right and useful and in accordance with the laws. Just as the laws are in charge of the magistrates, so the magistrates are in charge of the people; it can truly be said that a magistrate is a law that speaks, and a law is a silent magistrate. There is nothing so consonant with the justice and structure of nature – and when I say that, I want you to understand that I'm speaking of the law – as the power of command, without which no home or state or nation or the whole race of mankind can survive, nor can nature as a whole or the world itself. The world obeys god, and land and sea obey the world, and human life follows the commands of the supreme law. And to come to things closer and more familiar to us: all early peoples once obeyed kings. This type of power was first offered to the most just and wise men (as was particularly true of our own commonwealth, so long as monarchic power was in charge), and then it was handed on in turn to their descendants, a custom which remains in effect among contemporary monarchies.

  • Book 6

  • from On the Commonwealth
  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 93-104

  • Summary

    Cicero, Letters to Atticus 7.3.2: If I hadn't had that idea about a triumph, which you also approve of, then you wouldn't find me far short of that man who's described in the sixth book. Why should I be silent with you, who gobbled up those books? As it is, I won't have any doubts about abandoning so grand a thing, if it's better to do so; it's impossible for both to proceed together, to campaign for a triumph and to speak freely on public affairs.

    You're waiting for the complete foresight of this leader, which derives its name from seeing ahead. [+Nonius 42.3]

    Therefore this citizen must so prepare himself as always to be armed against things which disturb the stability of the state. [+Nonius 256.27]

    That discord of the citizens is called sedition because people go apart in following different leaders. [+Nonius 25.3]

    And in fact in a civil discord, when the respectable citizens are more important than the majority, I believe citizens should be weighed, not counted. [+Nonius 519.17]

    The passions exercise powerful control over thoughts; they compel and command innumerable things, and since they can't be fulfilled or satiated in any way, they drive to every sort of crime those whom they have inflamed with their enticements. [+Nonius 424.31]

    Who has beaten down its force and unbridled ferocity. [+Nonius 492.1]

    Which was all the greater, since, although the two colleagues were in the same position, they were not only not hated equally, but affection for Gracchus dispelled the hatred for Claudius. [+Aulus Gellius, Attic Nights 7.16.11 and Nonius 290.15]

    Whoever among the number of the best men and leading citizens has offered <aid to sedition?> abandons the solemn and dignified sound of his voice and respectability. [+Nonius 409.31]

    so that, as he writes, a thousand men should go down to the forum daily with cloaks dyed in purple [+Nonius 501.27]

    In their case, as you remember, the funeral was suddenly adorned by a crowd of the most insignificant people, collected with cash. [+Nonius 517.35]

    Our ancestors wanted marriages to be solidly established. [+Nonius 512.27 and Priscian 3.70.11K]

    The speech of Laelius, which we have all read, <shows> how pleasing to the immortal gods are the earthenware vessels of the priests and the sacrificial vessels (as he writes) of Samian pottery.

  • Book 2

  • from On the Laws
  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 131-158

  • Summary

    ATTICUS: Since we've already walked enough and you have to make a start on a new topic, why don't we move and sit down for the rest of the conversation on the island in the Fibrenus – I think that's the name of the other river?

    MARCUS: Certainly. I really enjoy using that spot regularly, whether I'm thinking something over or reading or writing something.

    ATTICUS: For my part, since I just now came here, I can't get enough of it: I have only contempt for grand villas and marble pavements and paneled ceilings. Those water-channels that some people call “Nile” or “Euripus” can only make you laugh when you've seen this spot. When you were speaking about law and justice a little while ago, you made nature the standard for everything; so too in seeking aids for mental relaxation and pleasure, nature is best. I used to wonder – I thought there was nothing around here but rocks and mountains, basing my opinion on your own speeches and poetry – I wondered, as I said, why you took such pleasure in this place. But now I wonder why, when you're away from Rome, you ever go anywhere else.

    MARCUS: When I can get away for some days, particularly at this season, I seek out the beauty and the healthfulness of this place – though that's not very often. But in fact I have another cause of pleasure here, which isn't so relevant to you.

    ATTICUS: What's that?

    MARCUS: Because, in truth, this is my own and my brother's real fatherland. Here is the most ancient origin of our stock; here are our family rituals and our family; here there are many traces of our ancestors. In brief: you see this house? It was made larger and fancier by the efforts of our father, who spent most of his life here in study, because of his poor health; but on this very spot, while my grandfather was still alive and it was a small house of the old style, like the house of Curius in the Sabine country, I was born. And so something abides deep in my mind and feelings, which makes me take all the more pleasure in this place, just as that wisest of men is said to have refused immortality so that he could see Ithaca again.

  • Book 4

  • from On the Commonwealth
  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 79-87

  • Summary

    … and finally that by its regular interposition it also creates the shade of night, something useful not only for the reckoning of days but for rest from toil. [+Nonius 234.14]

    And since in the autumn the earth has opened for the sowing of crops, in the winter has loosened up for preparing them, and in the ripeness of summer has softened some and parched others… [+Nonius 343.20]

    And the mind itself, which foresees the future, also remembers what is past. [+Nonius 500.9]

    Lactantius, On the Workmanship of God 1.11–13: Since reference has been made to the body and the mind, I will try to explain the rationale of each within the limited understanding of my feeble intelligence. I think it particularly important to take up this task, because Marcus Cicero, a man of outstanding talent, tried to do this in the fourth book of On the Commonwealth, but compressed a vast amount of material within a narrow compass and only touched lightly on the main points. Indeed he removes any excuse for not having dealt with the topic thoroughly by saying himself “that he had lacked neither the will nor the effort”: in the first book of On the Laws, when he was equally cursory on the same topic, he says: “As far as I am concerned, Scipio dealt adequately with this subject in the book which you have read” (1.27). Even so, he tried to give a fuller treatment of the same subject in the second book of On the Nature of the Gods.

    SCIPIO: * states, in which they seek the praise and respect of the best man, and flee shame and disgrace. But they aren't frightened so much by the fear and penalties established by law as by a sense of shame, which nature has given men as a sort of fear of criticism that is not undeserved. The leader of commonwealths strengthens this sense of shame by his opinions, and he brings it to perfection by institutions and education, so that shame does as much as fear to keep citizens from crime. These things are also relevant to praise, and they could be spoken on much more fully and elaborately.

  • Unplaced Fragments of On the Commonwealth

  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 105-106

  • Summary

    strive [Diomedes 1.339.31 K]

    they excel [Diomedes 1.374.17 K]

    Marius Victorinus, Commentary on Cicero's Rhetoric p.156.4–6 H: “Virtue” is identified by Cicero in his rhetorical works [i.e. De Inventione] with wisdom [sapientia], but elsewhere, in On the Commonwealth, it is said to be the same as judgment [prudentia].

    Lactantius, Inst. 1.18.11–13: In Ennius, Africanus says:

    If it is right for anyone to ascend into the tracts of the gods

    For me alone the greatest gate of heaven stands open.

    … Cicero agrees with this vanity, saying: “True enough, Africanus; that same gate stood open for Hercules.”

    Seneca, Moral Letters 108.32: When a grammarian explains the same text, he first reports that Cicero used the words reapse for re ipsa and sepse for se ipse, and then passes on to things that the custom of the times has altered, as when Cicero says: “since we have been called back by his summons from the very end of the race.” The ancients used the word calx [finish line] for what we now call creta in the circus.

    Anonymous Byzantine Dialogue on Politics, p.27.26–30 Mazzucchi: In saying this, Menodorus, you agree with Cicero, who says that it is proper for a king's entire thought to concern the selection of ten of the best men, who will be adequate and sufficient to make a selection of others whom they can use for the administration of the government.

  • Fragments of On the Laws

  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp 178-178

  • Summary

  • 1. We should count ourselves lucky, because death will bring us to a condition that is either better than that in life or at least no worse. If the soul is active without the body, then its life is divine; and if it has no sensation, then it is nothing bad. [Lactantius, Inst. 3.19.2]

  • 2. Since the sun has descended a little from mid-day, and this spot is not yet sufficiently shaded by these young trees, do you think we should go down to the Liris, and pursue the remainder of the conversation under the shade of those alders? [Macrobius, Saturnalia 5.4.8; from Book 5]

  • Text and Translation

  • Edited and translated by James E. G. Zetzel, Columbia University, New York
  • Marcus Tullius Cicero
  • Book:
    Cicero: <I>On the Commonwealth</I> and <I>On the Laws</I>
    Published online:
    14 September 2019
    Print publication:
    27 May 2017, pp xxix-xxxvi

  • Summary

    Powell 2006 contains critical editions of the Latin text of both On the Commonwealth and On the Laws; Ziegler 1969 and Ziegler 1979 edited them separately. Most of the continuous portions of On the Commonwealth are included in Zetzel 1995. Although I have relied on Ziegler and Powell for their reports of the manuscripts (which at times differ), this translation is based on my own construction of the Latin text. In On the Laws, I have generally followed Powell, whose edition is based on a better understanding of the manuscript tradition than Ziegler's; for On the Commonwealth, on the other hand, Powell's edition is very problematic. It is excellent in presenting words that are indubitably Cicero's own, and I have often followed his choices of reading, punctuation, and paragraphing. For those interested in Cicero's thought rather than his style, however, Powell is much less useful. Ziegler's text is not without problems, but his treatment of the fragments and testimonia as well as of the order of pages in the palimpsest is far superior to Powell's, and he is much more cautious – as is appropriate with a fragmentary text – in making arbitrary alterations and deletions. Ziegler's treatment of fragments and testimonia is at times confusing (or wrong), but Powell has arranged the material in a manner that makes it almost impossible to understand what Cicero is saying. The arrangement and presentation of the fragments is thus my own, but I have maintained Ziegler's numbering of paragraphs (which, at least for the palimpsest, is also reported by Powell), with the addition of lower-case letters to indicate separate fragments which Ziegler has grouped under a single paragraph number. The index of fragments, arranged by source, gives locations in Ziegler's and Powell's editions, and major textual differences from their editions are indicated in the notes.

Page 1311 of 1933