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 42
... shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
... shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA ...
Página 43
... shewn to be equal to it . Therefore , straight lines , & c . Q. E. D. PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are equal to one ano- ther , and the diameter bisects it that is , divides it into two equal ...
... shewn to be equal to it . Therefore , straight lines , & c . Q. E. D. PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are equal to one ano- ther , and the diameter bisects it that is , divides it into two equal ...
Página 44
... shewn to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two ...
... shewn to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two ...
Página 72
... shewn that FD is greater than CD . Therefore DA is the greatest ; and DE greater than DF , and DF than DC . And because MK , KD are greater ( 20. 1. ) than MD , and MK is equal to MG , the remainder KD is greater ( 5.Ax. ) than the ...
... shewn that FD is greater than CD . Therefore DA is the greatest ; and DE greater than DF , and DF than DC . And because MK , KD are greater ( 20. 1. ) than MD , and MK is equal to MG , the remainder KD is greater ( 5.Ax. ) than the ...
Página 75
... shewn , that a cir- cle cannot touch another on the inside in more than one point . Therefore , one circle , & c . QE . D. PROP . XIV . THEOR . B Equal straight lines in a circle are equally distant from the centre ; and those which are ...
... shewn , that a cir- cle cannot touch another on the inside in more than one point . Therefore , one circle , & c . QE . D. PROP . XIV . THEOR . B Equal straight lines in a circle are equally distant from the centre ; and those which are ...
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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