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 17
... common segment ; that is , they cannot " 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 ...
... common segment ; that is , they cannot " 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 ...
Página 24
... common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the re- maining angles of the ...
... common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the re- maining angles of the ...
Página 25
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the triangle DBC is equal to that of ...
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the triangle DBC is equal to that of ...
Página 27
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DAF is equal ( 8.1 . ) to the angle EAF : where- fore ...
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DAF is equal ( 8.1 . ) to the angle EAF : where- fore ...
Página 28
... common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal to the an- gle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB , and the ...
... common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal to the an- gle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB , and the ...
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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