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 σελίδες |
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Σελίδα 86
... 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 bisected in the point D. Ꭰ Because AC ... AC , CD are equal to the two BC , CD ...
... 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 bisected in the point D. Ꭰ Because AC ... AC , CD are equal to the two BC , CD ...
Σελίδα 101
... arches , therefore the arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the side of an equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe ...
... arches , therefore the arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the side of an equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe ...
Σελίδα 106
... AC be the side of an equilateral triangle inscribed ( 2. 4. ) in the circle , and AB the side of an equi- lateral ... arch ABC , being the third part of the whole contains five ; and the arch AB , which is the fifth part of the whole ...
... AC be the side of an equilateral triangle inscribed ( 2. 4. ) in the circle , and AB the side of an equi- lateral ... arch ABC , being the third part of the whole contains five ; and the arch AB , which is the fifth part of the whole ...
Σελίδα 151
... AC meets them , the alternate angles BAC , ACD are equal ( 29. 1. ) ; for the same reason , the angle CDE is equal ... arch BC to the arch EF , so is the angle BGC to the angle EHF , and the angle BAC to the angle EDF : and also the ...
... AC meets them , the alternate angles BAC , ACD are equal ( 29. 1. ) ; for the same reason , the angle CDE is equal ... arch BC to the arch EF , so is the angle BGC to the angle EHF , and the angle BAC to the angle EDF : and also the ...
Σελίδα 153
... arch BL be equal to EN , the sector BGL is equal to the sector EHN D G Η N K B M X E C F and if the arch BL be ... AC is equal to the rectangle BD.DC , together with the square of AD . B Describe the circle ( 5. 4. ) ACB about the ...
... arch BL be equal to EN , the sector BGL is equal to the sector EHN D G Η N K B M X E C F and if the arch BL be ... AC is equal to the rectangle BD.DC , together with the square of AD . B Describe the circle ( 5. 4. ) ACB about the ...
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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 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