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 σελίδες |
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Σελίδα 17
... coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the inter- sections of one superficies with another are also ...
... coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the inter- sections of one superficies with another are also ...
Σελίδα 21
... coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect one ...
... coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect one ...
Σελίδα 24
... coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is ...
... coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is ...
Σελίδα 27
... coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but have a different situation as EG and FG ...
... coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but have a different situation as EG and FG ...
Σελίδα 40
... coinciding with one an- other , which is impossible ( 11. Ax . ) The angles AGH I B D H F GHD therefore are not un- equal , that is , they are equal to one another . Now , the angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved to ...
... coinciding with one an- other , which is impossible ( 11. Ax . ) The angles AGH I B D H F GHD therefore are not un- equal , that is , they are equal to one another . Now , the angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved to ...
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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