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 sider |
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Side 124
... equimultiples . THE word equimultiple , one might imagine has its meaning fully afcertained , by the common acception of the two words of which it is made up ; and yet I cannot tell how it happens , that it it hardly ever conveys a ...
... equimultiples . THE word equimultiple , one might imagine has its meaning fully afcertained , by the common acception of the two words of which it is made up ; and yet I cannot tell how it happens , that it it hardly ever conveys a ...
Side 125
... equimultiples ; than which nothing can poffibly be more abfurd ; for it means only that the magnitudes are taken the fame number of times ; thus if any ftraight line , which you may call A be taken three times ; and call this BC and ...
... equimultiples ; than which nothing can poffibly be more abfurd ; for it means only that the magnitudes are taken the fame number of times ; thus if any ftraight line , which you may call A be taken three times ; and call this BC and ...
Side 126
... equimultiples or parts of a straight line the same may be readily transferred to triangles or pa- rallelograms , between the fame parallel lines ; to angles ; circumfe- rences and sectors of equal circles ; which I contend are all the ...
... equimultiples or parts of a straight line the same may be readily transferred to triangles or pa- rallelograms , between the fame parallel lines ; to angles ; circumfe- rences and sectors of equal circles ; which I contend are all the ...
Side 128
... equimultiples whatever of the bafe CD and of the triangle ACD ; I say that if the multiple of BC exceed the multiple ... equi- multiples and also any equi- But obferve we do multiples of 128 DISSERTATION VI .
... equimultiples whatever of the bafe CD and of the triangle ACD ; I say that if the multiple of BC exceed the multiple ... equi- multiples and also any equi- But obferve we do multiples of 128 DISSERTATION VI .
Side 129
... equimultiples of CB and of the triangle ABC . Again we are to take equimultiples any whatever of the fecond and fourth , of CD and of the triangle ACD : produce CD directly forward , and take DK , KL each equal to CD ; and in the fame ...
... equimultiples of CB and of the triangle ABC . Again we are to take equimultiples any whatever of the fecond and fourth , of CD and of the triangle ACD : produce CD directly forward , and take DK , KL each equal to CD ; and in the fame ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
Side 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.
Side 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.
Side 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.
Side 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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...