The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : 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 : to this Edition are Also Annexed, Elements of Plane and Spherical TrigonometryRobert Desilver, 1821 - 516 páginas |
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Página 195
... sphere is a solid figure described by the revolution of a se- micircle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the semicircle revolves . XVI . The centre of a sphere ...
... sphere is a solid figure described by the revolution of a se- micircle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the semicircle revolves . XVI . The centre of a sphere ...
Página 284
... sphere . Let the spheres be cut by a plane passing through the centre ; the common sections of it with the spheres shall be circles : be- cause the sphere is described by the revolution of a semicircle about the diameter remaining ...
... sphere . Let the spheres be cut by a plane passing through the centre ; the common sections of it with the spheres shall be circles : be- cause the sphere is described by the revolution of a semicircle about the diameter remaining ...
Página 286
... drants , and in the other hemisphere ; there shall be form- ed a solid polyhedron described in the sphere , composed of py- ramids , the bases of which are the aforesaid quadrilateral. 286 BOOK XII . THE ELEMENTS OF EUCLID .
... drants , and in the other hemisphere ; there shall be form- ed a solid polyhedron described in the sphere , composed of py- ramids , the bases of which are the aforesaid quadrilateral. 286 BOOK XII . THE ELEMENTS OF EUCLID .
Página 287
... sphere , the common vertex of them all being the point A ; and the superficies of this solid polyhedron does not meet the lesser sphere in which is the circle FGH : for , from the point A draw ( 11. 11. ) AZ perpendicular to the plane ...
... sphere , the common vertex of them all being the point A ; and the superficies of this solid polyhedron does not meet the lesser sphere in which is the circle FGH : for , from the point A draw ( 11. 11. ) AZ perpendicular to the plane ...
Página 288
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated ; from the point A draw AI perpendicular ...
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated ; from the point A draw AI perpendicular ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
AC is equal altitude angle ABC angle BAC base BC BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar solid angle solid parallelopipeds sphere spherical angle square of AC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Pasajes populares
Página 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 9 - 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 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 53 - 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 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Página 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.