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 25
... shewn to be equal to it . COR . 1. Hence , if two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2. And every quadrilateral ...
... shewn to be equal to it . COR . 1. Hence , if two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2. And every quadrilateral ...
Página 26
... 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 33
... shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ...
... shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ...
Página 61
... 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 . 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 ( 13. 1. ) than MD , and MK is equal to MG , the remainder KD is greater ( 5 . Ax . ) than the ...
Página 69
... 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 drawn at right ...
... 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 drawn at right ...
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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