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 TrigonometryW. E. Dean, 1835 - 316 páginas |
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Página 16
... reason , the exterior angle ČEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . B C PROP . XV . THEOR ...
... reason , the exterior angle ČEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . B C PROP . XV . THEOR ...
Página 22
... reason , GAC is equal to GDE ; there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I- H D B E The restriction of this ...
... reason , GAC is equal to GDE ; there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I- H D B E The restriction of this ...
Página 26
... base BC of the parallelogramis ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. 26 ELEMENTS.
... base BC of the parallelogramis ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ; wherefore AD is equal ( 1. 26 ELEMENTS.
Página 27
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . PROP . XXXI . THEOR . Triangles upon the same base , and between the same parallels , are equivalent to one another ...
... reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . PROP . XXXI . THEOR . Triangles upon the same base , and between the same parallels , are equivalent to one another ...
Página 30
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle ... reason , AB and AH are in the same straight line . F B D KLE H Now because the angle DBC is equal to the angle 30 ...
... reason , the triangle KGC is equal to the triangle KFC . Then , be- cause the triangle AEK is equal to the triangle ... reason , AB and AH are in the same straight line . F B D KLE H Now because the angle DBC is equal to the angle 30 ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob 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 plane polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle 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
Pasajes populares
Página 46 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 39 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 47 - 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 on the line between the points of section, is equal to the square on half the line.
Página 25 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Página 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 75 - 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 95 - 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 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 52 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Página 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.