A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for Exercise |
From inside the book
Page 163
... one another ; therefore the straight line AL is equal to BC . Where- fore from the given ... sides of the one equal to two sides of the other , each to each ; and have ... so that the point A may be on D , and the straight line AB upon DE ; the ...
... one another ; therefore the straight line AL is equal to BC . Where- fore from the given ... sides of the one equal to two sides of the other , each to each ; and have ... so that the point A may be on D , and the straight line AB upon DE ; the ...
Page 166
... upon the other side of the base CD are equal ( 3. 1. ) to one another ; but ... sides which are terminated in one extremity of the base equal to one another ... so that the point B be on E , and the straight line BC upon EF ; the point C ...
... upon the other side of the base CD are equal ( 3. 1. ) to one another ; but ... sides which are terminated in one extremity of the base equal to one another ... so that the point B be on E , and the straight line BC upon EF ; the point C ...
Page 176
... sides are opposite ; therefore the angle BHA is equal to the angle EFD ; but ... straight line falling upon two other straight lines makes the alternate angles equal to one ... may be demonstrated , that they do not meet towards A , C ; but ...
... sides are opposite ; therefore the angle BHA is equal to the angle EFD ; but ... straight line falling upon two other straight lines makes the alternate angles equal to one ... may be demonstrated , that they do not meet towards A , C ; but ...
Page 270
... Similar triangles are to one another in the duplicate ratio of their homo- logous sides . PROP , XX . THEOR . Similar polygons may ... so , by reason of the equiangular triangles BGH , DFE , is FD to FE ... upon a given straight line AB , a rec ...
... Similar triangles are to one another in the duplicate ratio of their homo- logous sides . PROP , XX . THEOR . Similar polygons may ... so , by reason of the equiangular triangles BGH , DFE , is FD to FE ... upon a given straight line AB , a rec ...
Page 271
... may be divided into the same number of similar tri- angles , having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides ... so EF to BG ; and ...
... may be divided into the same number of similar tri- angles , having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides ... so EF to BG ; and ...
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Common terms and phrases
ABC is equal altitude angle ABC angle BAC axis bisected centre circle ABCD circumference co-efficient cone conic section convergency curve cylinder described diameter divided draw equal angles equation equiangular equimultiples factors fluxion fore fraction geometrical progression given straight line gnomon greater Hence hyperbola join less Let ABC magnitudes multiple opposite parabola parallel parallelogram perpendicular plane angles polygon prism produced proportional pyramid Q. E. D. PROP Q. E. D. Proposition radius rectangle rectangle contained rectilineal figure remaining angle right angles segment shewn side BC similar sine solid angle solid parallelopiped spherical triangle square of AC subtract surd tang tangent Theorem third tiple triangle ABC vertex whence Wherefore
Popular passages
Page 172 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 191 - 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.
Page 190 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 196 - 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.
Page 192 - 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, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 177 - 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.
Page 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Page 286 - 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...
Page 179 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.