A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 pages |
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Page xi
... tangent to the curve , when conceived to be infinitely produced . Axiom , a self - evident truth , or a proposition immediately asserted to , when the terms of it are properly understood . Aris , in Geometry , the straight line in a ...
... tangent to the curve , when conceived to be infinitely produced . Axiom , a self - evident truth , or a proposition immediately asserted to , when the terms of it are properly understood . Aris , in Geometry , the straight line in a ...
Page xiii
... tangent to it , particularly the circle and its tangent . Continued Proportion , that in which the consequent of the first ratio is the same with the antecedent of the second , & c . Converging lines , such as continually approximate ...
... tangent to it , particularly the circle and its tangent . Continued Proportion , that in which the consequent of the first ratio is the same with the antecedent of the second , & c . Converging lines , such as continually approximate ...
Page xxv
... tangent of her orbit , which wss deduced from astronomical observation . The moon , therefore , has a tendency to descend toward the earth from the same cause that a stone at its sur- face has ; and if the descent of the stone in a ...
... tangent of her orbit , which wss deduced from astronomical observation . The moon , therefore , has a tendency to descend toward the earth from the same cause that a stone at its sur- face has ; and if the descent of the stone in a ...
Page xxvii
... tangent , which was known from the earth's rotation , it could be compared with the force of gravity at the same place , measured in like manner by the descent of a heavy body in its first moment of its fall . The precession , that is ...
... tangent , which was known from the earth's rotation , it could be compared with the force of gravity at the same place , measured in like manner by the descent of a heavy body in its first moment of its fall . The precession , that is ...
Page 221
... tangent DB . But if DCA does not pass through the centre of the circle ABC . take ( 1.3 . ) the centre E , and draw EF perpendicular ( 12. 1. ) to AC , and join EB , EC , ED : And because the straight line EF , which passe . through the ...
... tangent DB . But if DCA does not pass through the centre of the circle ABC . take ( 1.3 . ) the centre E , and draw EF perpendicular ( 12. 1. ) to AC , and join EB , EC , ED : And because the straight line EF , which passe . through the ...
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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.