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
... radius of the , circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15. 5. ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the ...
... radius of the , circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15. 5. ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the ...
Página 169
... radius therefore , as the radius of any circle to the semicircum ference , or as the diameter to the whole circumference , so is the square of the radius to the area of the circle . COR . 2. Hence a polygon may be described about a ...
... radius therefore , as the radius of any circle to the semicircum ference , or as the diameter to the whole circumference , so is the square of the radius to the area of the circle . COR . 2. Hence a polygon may be described about a ...
Página 173
... radius and the line made up of the radius and the perpendicular drawn from the centre on the chord of double that arch : And the chord of the arch is a mean pro- portional between the diameter and a line which is the difference between ...
... radius and the line made up of the radius and the perpendicular drawn from the centre on the chord of double that arch : And the chord of the arch is a mean pro- portional between the diameter and a line which is the difference between ...
Página 174
... radius and the line made up of the radius , and the perpendicular on the chord of twice the arch BD . Again , it is evident , that BD is a mean proportional between AB and BF ( 8. 6. ) , that is , between the diameter and the excess of ...
... radius and the line made up of the radius , and the perpendicular on the chord of twice the arch BD . Again , it is evident , that BD is a mean proportional between AB and BF ( 8. 6. ) , that is , between the diameter and the excess of ...
Página 175
... radius , and the line AF . Now because the sides BD , DC , of the triangle BDC are equal , the angles DCF , DBF are ... radius contains 1000 . = - But by the last proposition , the chord of one ninety - sixth part of the circumference is ...
... radius , and the line AF . Now because the sides BD , DC , of the triangle BDC are equal , the angles DCF , DBF are ... radius contains 1000 . = - But by the last proposition , the chord of one ninety - sixth part of the circumference is ...
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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