The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 140
... prism . The prism is , for geometrical purposes , considered as capable of indefinite prolongation both ways from the parallel planes , or in the direction of the lines . The lines are called the edges of the prism ; the parallel planes ...
... prism . The prism is , for geometrical purposes , considered as capable of indefinite prolongation both ways from the parallel planes , or in the direction of the lines . The lines are called the edges of the prism ; the parallel planes ...
Σελίδα 154
... prism or pyramid parallel to the base is similar to the base ; and that of the prism also equal to the base . ( 1. ) Let ABCDE be the base of a prism , and the prism itself be cut by a plane parallel thereto in abcde : then the figure ...
... prism or pyramid parallel to the base is similar to the base ; and that of the prism also equal to the base . ( 1. ) Let ABCDE be the base of a prism , and the prism itself be cut by a plane parallel thereto in abcde : then the figure ...
Σελίδα 193
... prisms - sometimes even to include these amongst the former . ( 3. ) To divide every polyhedron into parallelopipeds or prisms ( most commonly the latter ) , and then assign a rectangular parallelo- piped equal to the sum of them all ...
... prisms - sometimes even to include these amongst the former . ( 3. ) To divide every polyhedron into parallelopipeds or prisms ( most commonly the latter ) , and then assign a rectangular parallelo- piped equal to the sum of them all ...
Σελίδα 194
... prism be equal to one triangular prism and symmetrical to another , these latter prisms contain equal volumes of space . " The case of the parallelopiped can be proved from this , or rather it is a mere corollary . Indeed we are ...
... prism be equal to one triangular prism and symmetrical to another , these latter prisms contain equal volumes of space . " The case of the parallelopiped can be proved from this , or rather it is a mere corollary . Indeed we are ...
Σελίδα 195
... prisms therefore coinciding , they the same space , " and are therefore equal . " fill ( 2. ) Let the two prisms be symmetrical : then by the axiom , they are of equal volume . We give the figure for illustration . F E A FI B ...
... prisms therefore coinciding , they the same space , " and are therefore equal . " fill ( 2. ) Let the two prisms be symmetrical : then by the axiom , they are of equal volume . We give the figure for illustration . F E A FI B ...
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ABCD axis base bisected called centre circle circumference coincide common cone construction contained coordinate curve described diameter difference dihedral angles direction distance divided double draw drawn edges ellipse equal equal angles equimultiples extremities faces figure formed four fourth given line given point greater hence horizontal inclination intersection join less likewise magnitudes manner meet method multiple opposite parallel parallelogram pass perpendicular perspective picture plane MN plane of projection position preceding prisms problem produced projector Prop proportional PROPOSITION proved ratio reason rectangle remaining respectively right angles SCHOLIUM segment shown sides similar sphere square straight line surface taken tangent THEOR third touch trace transverse triangle triangle ABC trihedral vertex vertical Whence Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 35 - 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.
Σελίδα 4 - AB; but things which are equal to the same are equal to one another...
Σελίδα 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 8 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Σελίδα 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Σελίδα 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 116 - 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.