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 85
... arches , when they are at the centres ; therefore the arch BGC is equal to the arch EHF . But the whole circle ABC is equal to the whole EDF ; the remaining part , therefore , of the circumference , viz . BAC , is equal to the remaining ...
... arches , when they are at the centres ; therefore the arch BGC is equal to the arch EHF . But the whole circle ABC is equal to the whole EDF ; the remaining part , therefore , of the circumference , viz . BAC , is equal to the remaining ...
Página 86
... arch , that is , to divide it into two equal parts , Let ADB be the given arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and join AD , DB : the arch ADB is ...
... arch , that is , to divide it into two equal parts , Let ADB be the given arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and join AD , DB : the arch ADB is ...
Página 87
... arch BD , and join AD , DC , CB ; and because the straight line EF touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line , from the point of contact B , the centre of the circle is ( 19. 3. ) in ...
... arch BD , and join AD , DC , CB ; and because the straight line EF touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line , from the point of contact B , the centre of the circle is ( 19. 3. ) in ...
Página 101
... arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the ... arch AB is equal to the arch DE ; if to each be add- ed BCD , the whole ABCD is equal to the whole EDCB : and the ...
... arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the ... arch AB is equal to the arch DE ; if to each be add- ed BCD , the whole ABCD is equal to the whole EDCB : and the ...
Página 102
... arches cut off will be one - tenth of the circumference , and " therefore the arch made up of both will be one - fifth of the circum- " ference ; and if the straight line subtending this arch be drawn it " will be the side of an ...
... arches cut off will be one - tenth of the circumference , and " therefore the arch made up of both will be one - fifth of the circum- " ference ; and if the straight line subtending this arch be drawn it " will be the side of an ...
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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