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 TrigonometryCollins & Hannay, 1860 - 333 σελίδες |
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Σελίδα 110
... Prop . 16. of this Book . XV . Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth to the third . Prop . A. Book 5 . XVI . Componendo , by composition ...
... Prop . 16. of this Book . XV . Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth to the third . Prop . A. Book 5 . XVI . Componendo , by composition ...
Σελίδα 319
... Prop . A is given immediately after the third , being , in fact , a second case of that pro- position , and capable of being included with it , in one enunciation . Prop . D. is remarkable for being a theorem of Ptolemy the Astrono- mer ...
... Prop . A is given immediately after the third , being , in fact , a second case of that pro- position , and capable of being included with it , in one enunciation . Prop . D. is remarkable for being a theorem of Ptolemy the Astrono- mer ...
Σελίδα 332
... ( Prop . 1. ) in the right angled triangle BCD , BC : CD :: R : tan CBD , CBD is the angle of which the tangent is D 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 . 1 ...
... ( Prop . 1. ) in the right angled triangle BCD , BC : CD :: R : tan CBD , CBD is the angle of which the tangent is D 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 . 1 ...
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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 and similar 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 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore