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 23
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are ... base BC be equal to the base EF ; and , the triangle ABC to the tri- angle DEF ; and the D other angles , to which B E F ...
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are ... base BC be equal to the base EF ; and , the triangle ABC to the tri- angle DEF ; and the D other angles , to which B E F ...
Σελίδα 24
... base BC shall coincide with the base EF ( cor . def 3 , ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal and ...
... base BC shall coincide with the base EF ( cor . def 3 , ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal and ...
Σελίδα 25
... BC 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 ...
... BC 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 ...
Σελίδα 27
... base BC equal to the base EF . The angle BAC is equal 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 ...
... base BC equal to the base EF . The angle BAC is equal 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 ...
Σελίδα 28
... 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 straight line AB is divided into two equal parts in the point D. Which was to be done ...
... 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 straight line AB is divided into two equal parts in the point D. Which was to be done ...
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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