The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfthA. Foulis, 1781 - 466 páginas |
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Página 189
... Sphere is a folid figure described by the revolution of a semi- circle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the se- micircle revolves . XVI . The center of a sphere ...
... Sphere is a folid figure described by the revolution of a semi- circle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the se- micircle revolves . XVI . The center of a sphere ...
Página 278
... sphere . Let the spheres be cut by a plane passing thro ' the center ; the common fections of it with the spheres shall be circles ; because the sphere is defcribed by the revolution of a femicircle about the dia- meter remaining ...
... sphere . Let the spheres be cut by a plane passing thro ' the center ; the common fections of it with the spheres shall be circles ; because the sphere is defcribed by the revolution of a femicircle about the dia- meter remaining ...
Página 280
... BK , and the like be done alfo in the other three quadrants , and in the other hemisphere ; there shall be formed a folid polyhedron defcribed in the sphere , composed of pyramids the bases of which are the aforesaid 280 ELEMENTS THE.
... BK , and the like be done alfo in the other three quadrants , and in the other hemisphere ; there shall be formed a folid polyhedron defcribed in the sphere , composed of pyramids the bases of which are the aforesaid 280 ELEMENTS THE.
Página 281
... sphere , the common vertex of them all being the point A. and the fuperficies of this folid polyhedron does - not meet the lesser sphere in which is the circle FGH . for from the point A draw k AZ perpendicular to the plane of the ...
... sphere , the common vertex of them all being the point A. and the fuperficies of this folid polyhedron does - not meet the lesser sphere in which is the circle FGH . for from the point A draw k AZ perpendicular to the plane of the ...
Página 282
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . 12 . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated . from the point A draw Al ...
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . 12 . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated . from the point A draw Al ...
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Términos y frases comunes
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs faid fame multiple fame ratio fame reaſon fegment fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs line BC oppoſite parallel parallelepipeds parallelogram paſs perpendicular proportionals Propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſhall ſhall be equal ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro tiple triangle ABC vertex wherefore
Pasajes populares
Página 156 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 3 - 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Página 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Página 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Página 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...