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 páginas |
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Página 82
... segments of circles upon the equal straight lines AB , CD ; the segment AEB is equal to the segment CFD . For , if the segment AEB be applied to the segment CFD , so as the point A be on C , and the straight line AB upon CD , the point ...
... segments of circles upon the equal straight lines AB , CD ; the segment AEB is equal to the segment CFD . For , if the segment AEB be applied to the segment CFD , so as the point A be on C , and the straight line AB upon CD , the point ...
Página 84
... segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore , the segment BA is ...
... segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore , the segment BA is ...
Página 89
... segment AHB of a circle is described which contains an angle equal to the given angle at C. Which was to be done . PROP . XXXIV . PROB . To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal ...
... segment AHB of a circle is described which contains an angle equal to the given angle at C. Which was to be done . PROP . XXXIV . PROB . To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal ...
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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