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 7
... BAC , BAG , BAE ; FAC , FAG , FAE ; DAC , DAG , DAE ; are only fo many different ways of expreffing the fame angle , nor does this great variety , in the least puzzle or perplex the conceptions of an adept . This looks fo much like a ...
... BAC , BAG , BAE ; FAC , FAG , FAE ; DAC , DAG , DAE ; are only fo many different ways of expreffing the fame angle , nor does this great variety , in the least puzzle or perplex the conceptions of an adept . This looks fo much like a ...
Side 35
... angle contained by BAC equal to the angle contained by EDF . B CE F This now is the hypothefis or fuppofition , which is to be con- fidered as abfolutely certain ; and a principle from which we are to reason as confidently , as from the ...
... angle contained by BAC equal to the angle contained by EDF . B CE F This now is the hypothefis or fuppofition , which is to be con- fidered as abfolutely certain ; and a principle from which we are to reason as confidently , as from the ...
Side 37
... angle BAC be equal to the angle EDF ; because when the point A is upon the point D : and AB upon DE ; it follows from the equality of the angles that AC will take the direction of DF . But if the angles be unequal , although the point A ...
... angle BAC be equal to the angle EDF ; because when the point A is upon the point D : and AB upon DE ; it follows from the equality of the angles that AC will take the direction of DF . But if the angles be unequal , although the point A ...
Side 39
... angle BAC equal to the angle EDF ; but moreover , that AB is equal to AC and confequently DE to DF : now by placing the triangles as in the propofition , we fhall find the angle ABC equal to DEF ; and not only that , but , by putting A ...
... angle BAC equal to the angle EDF ; but moreover , that AB is equal to AC and confequently DE to DF : now by placing the triangles as in the propofition , we fhall find the angle ABC equal to DEF ; and not only that , but , by putting A ...
Side 41
... angle BAC be equal to EDF , the line AC must take the direction of DF ; and it is im- poffible to conceive it to ... angle contained by the fides is any particular angle , but only that the angles are equal . And this may fuffice for an ...
... angle BAC be equal to EDF , the line AC must take the direction of DF ; and it is im- poffible to conceive it to ... angle contained by the fides is any particular angle , but only that the angles are equal . And this may fuffice for an ...
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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...