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, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 108
... PROP . IX . THEOR . Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the sarne ratio are equal to one another . If A : C : B : C , A = B . For if not , let A ...
... PROP . IX . THEOR . Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the sarne ratio are equal to one another . If A : C : B : C , A = B . For if not , let A ...
Página 299
... Prop . A is given immediately after the third , being , in fact , a second case of that proposition , and capable of being included with it , in one enunciation . Prop . D is remarkable for being a theorem of Ptolemy the Astronomer , in ...
... Prop . A is given immediately after the third , being , in fact , a second case of that proposition , and capable of being included with it , in one enunciation . Prop . D is remarkable for being a theorem of Ptolemy the Astronomer , in ...
Página 311
... ( Prop . 1. ) in the right angled D triangle BCD , BC : CD :: R : tan CBD , CBD is the angle of which the tangent is to the radius as CD to BC , that is , as CA to BC , or as the least of the two sides of the triangle to the greatest ...
... ( Prop . 1. ) in the right angled D triangle BCD , BC : CD :: R : tan CBD , CBD is the angle of which the tangent is to the radius as CD to BC , that is , as CA to BC , or as the least of the two sides of the triangle to the greatest ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC wherefore