Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 35
... base DE to the base FG ; the angle DCE is equal ( 8. 1. ) to the angle FAG . Therefore , at the given point A in OF GEOMETRY . BOOK I. 335.
... base DE to the base FG ; the angle DCE is equal ( 8. 1. ) to the angle FAG . Therefore , at the given point A in OF GEOMETRY . BOOK I. 335.
Página 36
... base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to each viz . AB equal to DE , and AC to DF ; but the ...
... base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to each viz . AB equal to DE , and AC to DF ; but the ...
Página 37
... base CB be greater than the base EF , the angle BAC is likewise greater than the angle EDF . For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base ...
... base CB be greater than the base EF , the angle BAC is likewise greater than the angle EDF . For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base ...
Página 38
... base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles are equal , each to each , to which the equal sides are opposite ; therefore the angle BHA is equal to the angle EFD ; but EFD is equal to ...
... base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles are equal , each to each , to which the equal sides are opposite ; therefore the angle BHA is equal to the angle EFD ; but EFD is equal to ...
Página 43
... base AC is equal ( 4. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles ( 4. 1. ) each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the ...
... base AC is equal ( 4. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles ( 4. 1. ) each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore