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 TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Σελίδα 12
... fore CA is equal to CB ; wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight ...
... fore CA is equal to CB ; wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight ...
Σελίδα 17
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . D E F B C By the same construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a ...
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . D E F B C By the same construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a ...
Σελίδα 30
... fore also the angles CBA , BAC , ACB are equal to two right angles . D COR . 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides , wanting four right angles . For any ...
... fore also the angles CBA , BAC , ACB are equal to two right angles . D COR . 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides , wanting four right angles . For any ...
Σελίδα 33
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
Σελίδα 35
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the parallelogram ...
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the parallelogram ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore