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 40
... interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle KGH equal to GHD ...
... interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle KGH equal to GHD ...
Página 41
... interior and opposite angles ; and the three interior angles of eve- ry triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior ...
... interior and opposite angles ; and the three interior angles of eve- ry triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior ...
Página 42
... interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and ...
... interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and ...
Página 44
... are equal to the two DE FA E D F B C B C FD , DC , each to each ; but the exterior angle FDC is equal ( 29. 1. ) e interior EAB , wherefore the base EB is equal to the base FC , to and the triangle EAB ( 4. 1. ) to the 44 ELEMENTS.
... are equal to the two DE FA E D F B C B C FD , DC , each to each ; but the exterior angle FDC is equal ( 29. 1. ) e interior EAB , wherefore the base EB is equal to the base FC , to and the triangle EAB ( 4. 1. ) to the 44 ELEMENTS.
Página 49
... interior angles , upon the same side , less than two right angles , do meet if produced ( Cor . 29. 1. ) : Therefore HB , FE will meet , if produced ; let them meet in K , and through K draw KL parallel to EA or FH , and produce HA , GB ...
... interior angles , upon the same side , less than two right angles , do meet if produced ( Cor . 29. 1. ) : Therefore HB , FE will meet , if produced ; let them meet in K , and through K draw KL parallel to EA or FH , and produce HA , GB ...
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Términos y frases comunes
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