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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 páginas |
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Página 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 ...
Página 17
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . DA 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 ...
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . DA 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 ...
Página 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 ...
Página 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 ...
Página 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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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition 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 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
Pasajes populares
Página 41 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 70 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Página 91 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...