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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 16
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . PROP . XV . THEOR ...
... reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . PROP . XV . THEOR ...
Página 22
... reason , GAC is equal to GDE ; there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I H D B The restriction of this ...
... reason , GAC is equal to GDE ; there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I H D B The restriction of this ...
Página 26
... base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. 26 ELEMENTS.
... base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. 26 ELEMENTS.
Página 27
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Triangles upon PROP . XXXI . THEOR . the same base , and between the same parallels , are equivalent to one another ...
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Triangles upon PROP . XXXI . THEOR . the same base , and between the same parallels , are equivalent to one another ...
Página 30
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle ... reason , AB and AH are in the same straight line . F G H K B C of OUA ON De L E ofni Now because the angle DBC is ...
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle ... reason , AB and AH are in the same straight line . F G H K B C of OUA ON De L E ofni Now because the angle DBC is ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore