## The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 Seiten |

### Im Buch

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**himself**could have fully gratified , by condescending a little to the weakness of his readers , and rescued his works out of such clumfy hands . What apology therefore shall I be able to make for loading with a commentary the most ... Seite 2

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**himself**in fuch a manner as to be always in- telligible even to those whom he would wish to have for readers . Because authors are confined to a particular method of arrangement , if it be their intention to deliver opinions or ... Seite 3

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**himself**master of the subject and not incumbered with all those particular instances , which would now stand in the way of the readers imagination as much as they affifted it before . For instance , who could relish the nobleft of ... Seite 4

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**himself**to be understood . An oftentation of learning is a fault which prevails among many commentators ; for they feem to be apprehensive least the world should think they know nothing but their bufinefs and therefore instead of ... Seite 5

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**himself**with a ruler and compaffes , and after fome practice in drawing ftraight lines , and defcribing circles ; he is next to proceed to the examination of the common notions , as if they were properties of ftraight lines only , and ...### Andere Ausgaben - Alle anzeigen

The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |

### Häufige Begriffe und Wortgruppen

ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe

### Beliebte Passagen

Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.

Seite 47 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Seite 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.

Seite 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.

Seite 15 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...

Seite 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Seite 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.

Seite 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.

Seite 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...