The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 4
... a learned gentleman . To which are also added , the Elements of Plane and Spherical Trigono- metry , which are commonly taught after the Elements of Euclid . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. iv PREFACE .
... a learned gentleman . To which are also added , the Elements of Plane and Spherical Trigono- metry , which are commonly taught after the Elements of Euclid . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. iv PREFACE .
Página 156
... sphere is a solid figure described by the revolution of a semicircle about its diameter , which remains unmoved . XV . · The axis of a sphere is the fixed straight line about which the semi- circle revolves . XVI . The centre of a sphere ...
... sphere is a solid figure described by the revolution of a semicircle about its diameter , which remains unmoved . XV . · The axis of a sphere is the fixed straight line about which the semi- circle revolves . XVI . The centre of a sphere ...
Página 227
... sphere . Let the spheres be cut by a plane passing through the centre ; the common sections of it with the spheres shall be circles : because the sphere is described by the revolution of a semicircle about the diame- ter 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 : because the sphere is described by the revolution of a semicircle about the diame- ter remaining ...
Página 228
... sphere ; and let BXD , KXN be the semicir- cles thus made upon the diameters BD , KN : therefore , because XA is at right angles to the plane of the circle BCDE , every plane which passes through XA is at right ( 18. 11. ) angles to the ...
... sphere ; and let BXD , KXN be the semicir- cles thus made upon the diameters BD , KN : therefore , because XA is at right angles to the plane of the circle BCDE , every plane which passes through XA is at right ( 18. 11. ) angles to the ...
Página 229
... there shall be formed a solid polyhedron described in the sphere , composed of pyramids , the bases of which are the aforesaid quadrilateral figures 230 THE ELEMENTS OF EUCLID . and the triangle YRX BOOK XII . 229 THE ELEMENTS OF EUCLID .
... there shall be formed a solid polyhedron described in the sphere , composed of pyramids , the bases of which are the aforesaid quadrilateral figures 230 THE ELEMENTS OF EUCLID . and the triangle YRX BOOK XII . 229 THE ELEMENTS OF EUCLID .
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal 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 gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC 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 sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 63 - 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 246 - 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 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 119 - 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 19 - 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 12 - 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.
Página 78 - 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 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.