Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite 17
... coincide in part , without coinciding altogether . 66 " " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and " the intersections of one superficies with another are ...
... coincide in part , without coinciding altogether . 66 " " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and " the intersections of one superficies with another are ...
Seite 23
... coincide with one another , that is , which exactly fill the same space , are equal to one ano- ther . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect ...
... coincide with one another , that is , which exactly fill the same space , are equal to one ano- ther . IX . The whole is greater than its part . X. All right angles are equal to one another . XI . " Two straight lines which intersect ...
Seite 26
... 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 equal to DF : But the point B coincides with the point E ; wherefore the base BC 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 equal to DF : But the point B coincides with the point E ; wherefore the base BC shall ...
Seite 27
... coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the one equal to two sides of the other ...
... coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the one equal to two sides of the other ...
Seite 30
... to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the · point F , because BC is equal to EF 30 ELEMENTS.
... to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the · point F , because BC is equal to EF 30 ELEMENTS.
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB proportional 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 SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore