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 TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página xiv
... proved . Indeed , those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
... proved . Indeed , those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
Página 22
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
Página 24
... AFCto the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remainder BF shall be D / equal ( 3. Ax . ) to the remainder CG ; A B C F G E and FC was proved to be equal to GB , 24 ELEMENTS.
... AFCto the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remainder BF shall be D / equal ( 3. Ax . ) to the remainder CG ; A B C F G E and FC was proved to be equal to GB , 24 ELEMENTS.
Página 25
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are ...
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are ...
Página 26
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
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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 opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced 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 parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore