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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 45
... manner , EH = A.EC . Therefore A.BC = A : BD + A.DE + A.EC ; that is , the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A.EC. SCHOLIUM . The properties of the sections of lines , demonstrated in this Book , are easily ...
... manner , EH = A.EC . Therefore A.BC = A : BD + A.DE + A.EC ; that is , the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A.EC. SCHOLIUM . The properties of the sections of lines , demonstrated in this Book , are easily ...
Página 61
... manner it may be 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 ( 13. 1. ) than MD , and MK is equal to MG , the remainder KD is greater ( 5 ...
... manner it may be 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 ( 13. 1. ) than MD , and MK is equal to MG , the remainder KD is greater ( 5 ...
Página 69
... manner it may be shewn , that no other line but FC can be perpendicular to DE ; FC is therefore perpendicular to DE . F B D G E PROP . XIX . THEOR . If a straight line touch a circle , and from the point of contact a straight line be ...
... manner it may be shewn , that no other line but FC can be perpendicular to DE ; FC is therefore perpendicular to DE . F B D G E PROP . XIX . THEOR . If a straight line touch a circle , and from the point of contact a straight line be ...
Página 70
... manner it may be shewn , that no other point which is not in CA , is the centre ; that is , the centre is in CA. B D F PROP . XX . THEOR . The angle at the centre of a circle is double of the angle at the circumference , the same base ...
... manner it may be shewn , that no other point which is not in CA , is the centre ; that is , the centre is in CA. B D F PROP . XX . THEOR . The angle at the centre of a circle is double of the angle at the circumference , the same base ...
Página 71
... ) ; therefore also the B angles ABC , ADC are equal to two right angles ; In the same manner , the angles BAD , DCB may be shewn to be equal to two right angles . COR . 1. If any side of a quadrilateral be OF GEOMETRY . BOOK III . 71.
... ) ; therefore also the B angles ABC , ADC are equal to two right angles ; In the same manner , the angles BAD , DCB may be shewn to be equal to two right angles . COR . 1. If any side of a quadrilateral be OF GEOMETRY . BOOK III . 71.
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore