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 78
... touches the circle ; and B E C H A D that it touches it only in one point ; because , if it did meet the circle in two , it would fall within it ( 2. 3. ) . Also it is evident that there can be but one straight line which touches the ...
... touches the circle ; and B E C H A D that it touches it only in one point ; because , if it did meet the circle in two , it would fall within it ( 2. 3. ) . Also it is evident that there can be but one straight line which touches the ...
Σελίδα 90
... touches it the rectangle contain- ed by the whole line which cuts the circle , and the part of it without the circle , is equal to the square of the line which touches it . Let D be any point without the circle ABC , and DCA , DB two ...
... touches it the rectangle contain- ed by the whole line which cuts the circle , and the part of it without the circle , is equal to the square of the line which touches it . Let D be any point without the circle ABC , and DCA , DB two ...
Σελίδα 92
... touches the circle ABC , and DCA cuts it , the rectangle AD.DC is equal ( 36. 3. ) to the square of DE ; but the ... touches ( 16. 3. ) the circle : there- fore DB touches the circle ABC . Where- fore , if from a point , & c . Q. E. D. ...
... touches the circle ABC , and DCA cuts it , the rectangle AD.DC is equal ( 36. 3. ) to the square of DE ; but the ... touches ( 16. 3. ) the circle : there- fore DB touches the circle ABC . Where- fore , if from a point , & c . Q. E. D. ...
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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