A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 páginas |
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Página xvi
... drawn to four lines given in position , a given function of these perpendiculars , in which the variable quantities are only of two di- mensions , shall be always of the same magnitude . Descartes shows the locus , on this hypothesis ...
... drawn to four lines given in position , a given function of these perpendiculars , in which the variable quantities are only of two di- mensions , shall be always of the same magnitude . Descartes shows the locus , on this hypothesis ...
Página 168
... drawn at right angles to AB . Which was to be done . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . D If it be possible , let the two straight lines ABC , ABD have the seg ...
... drawn at right angles to AB . Which was to be done . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . D If it be possible , let the two straight lines ABC , ABD have the seg ...
Página 201
... drawn from any point in the circumference of the segment , to the extremities of the straight line , which is the base of the segment . 9. And an angle is said to insist or stand upon the circumference intercepted between the straight ...
... drawn from any point in the circumference of the segment , to the extremities of the straight line , which is the base of the segment . 9. And an angle is said to insist or stand upon the circumference intercepted between the straight ...
Página 202
... drawn from A to B shall fall within the circle . For , if it do not , let it fall , if possible , without , as AEB ; find , ( 1. 3. ) D the centre of the circle ABC , and join AD , DB , and produce DF , any straight line meeting the ...
... drawn from A to B shall fall within the circle . For , if it do not , let it fall , if possible , without , as AEB ; find , ( 1. 3. ) D the centre of the circle ABC , and join AD , DB , and produce DF , any straight line meeting the ...
Página 204
... drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line which passes through the centre is always ...
... drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line which passes through the centre is always ...
Índice
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xvi | |
xvi | |
xvi | |
xxvi | |
19 | |
97 | |
108 | |
120 | |
149 | |
159 | |
344 | |
367 | |
387 | |
397 | |
404 | |
410 | |
417 | |
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426 | |
437 | |
447 | |
576 | |
577 | |
588 | |
607 | |
627 | |
637 | |
651 | |
663 | |
673 | |
687 | |
694 | |
703 | |
709 | |
Palavras e frases frequentes
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
Passagens conhecidas
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Página 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...
Página 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.