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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 165
... difference between them shall be less than the square of D. In the circle ABC apply the straight line AE equal to D , and let AB be a fourth part of the circumference of the circle . From the cir- cumference AB take away its half , and ...
... difference between them shall be less than the square of D. In the circle ABC apply the straight line AE equal to D , and let AB be a fourth part of the circumference of the circle . From the cir- cumference AB take away its half , and ...
Página 167
... difference of the polygons ( 14. 5 ) . The difference of the poly- gons is therefore less than the square of AF ; but AF is less than D ; therefore , the difference of the polygons is less than the square of D , that is , than the given ...
... difference of the polygons ( 14. 5 ) . The difference of the poly- gons is therefore less than the square of AF ; but AF is less than D ; therefore , the difference of the polygons is less than the square of D , that is , than the given ...
Página 169
... difference between half the perimeter of the polygon whose side is EF , and half the cir- cumference of the circle : therefore , twice HL is the difference be- tween the whole perimeter of the polygon and the whole circumfer- ence of ...
... difference between half the perimeter of the polygon whose side is EF , and half the cir- cumference of the circle : therefore , twice HL is the difference be- tween the whole perimeter of the polygon and the whole circumfer- ence of ...
Página 173
... difference between the radius and the foresaid perpendicular from the centre . Let ADB be a circle , of which the centre is C ; DBE any arch , and DB the half of it ; let the chords DE , DB be drawn ; as also CF and CG at right angles ...
... difference between the radius and the foresaid perpendicular from the centre . Let ADB be a circle , of which the centre is C ; DBE any arch , and DB the half of it ; let the chords DE , DB be drawn ; as also CF and CG at right angles ...
Página 177
... or as 71 to 223 , so the given diameter to a fourth proportional , this will be nearly equal to the circumference , but will be less than it , ? 1 COR . 2. Because the difference between and 7 OF GEOMETRY . BOOK I. 177 .
... or as 71 to 223 , so the given diameter to a fourth proportional , this will be nearly equal to the circumference , but will be less than it , ? 1 COR . 2. Because the difference between and 7 OF GEOMETRY . BOOK I. 177 .
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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 multiple opposite angle parallel parallelepipeds 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 shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore