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 15
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
Página 16
... third side , the two sides BA , AE of the trian- gle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE , EC : Again , be- cause the two sides CE , ED , of the triangle CED are greater ...
... third side , the two sides BA , AE of the trian- gle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are greater than BE , EC : Again , be- cause the two sides CE , ED , of the triangle CED are greater ...
Página 18
... third sides BC and EF were equal . If possible , suppose that those sides are not equal , and that BC is the greater . Take BH - EF ; and join AH . The triangle ABH = DEF ; for the right angles B and E are equal , 18 ELEMENTS.
... third sides BC and EF were equal . If possible , suppose that those sides are not equal , and that BC is the greater . Take BH - EF ; and join AH . The triangle ABH = DEF ; for the right angles B and E are equal , 18 ELEMENTS.
Página 20
... third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and ...
... third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and ...
Página 23
... third will be found by subtracting that sum from two right angles . COR . 2. If two angles of one triangle are respectively equal to two an- gles of another , the third angles will also be equal , and the two triangles will be mutually ...
... third will be found by subtracting that sum from two right angles . COR . 2. If two angles of one triangle are respectively equal to two an- gles of another , the third angles will also be equal , and the two triangles will be mutually ...
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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