A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 Seiten |
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Seite xii
... magnitudes , such as have some com- mon aliquot part , or which may be measured or divided without a remainder , by the same measure or divisor . Common , applied to an angle , line , measure , or the like , that be- longs to two or ...
... magnitudes , such as have some com- mon aliquot part , or which may be measured or divided without a remainder , by the same measure or divisor . Common , applied to an angle , line , measure , or the like , that be- longs to two or ...
Seite xvi
... magnitudes both similar and equal . This principle , which is quite general with respect to recti- lineal figures , must fail , when we would compare curvilineal and rectilineal spaces with one another , and make the latter serve as ...
... magnitudes both similar and equal . This principle , which is quite general with respect to recti- lineal figures , must fail , when we would compare curvilineal and rectilineal spaces with one another , and make the latter serve as ...
Seite xvi
... magnitude . Descartes shows the locus , on this hypothesis , to be always a conic section ; and he distinguishes the ... magnitudes , or by what may be called natural signs ; a line by a line , an angle by an angle , an area by an area ...
... magnitude . Descartes shows the locus , on this hypothesis , to be always a conic section ; and he distinguishes the ... magnitudes , or by what may be called natural signs ; a line by a line , an angle by an angle , an area by an area ...
Seite xvi
... magnitudes themselves might be represented by figures , as in geometry , as well as in any way whatever ; but the operations they are to be subjected to , if described in words , must be set before the mind slowly , and in succession ...
... magnitudes themselves might be represented by figures , as in geometry , as well as in any way whatever ; but the operations they are to be subjected to , if described in words , must be set before the mind slowly , and in succession ...
Seite xvi
... magnitudes , makes the foregoing application of them infinitely more extensive and more indispensable . In the end of the sixteenth century , the time and labour consumed in astronomical and other calculations had become excessive , and ...
... magnitudes , makes the foregoing application of them infinitely more extensive and more indispensable . In the end of the sixteenth century , the time and labour consumed in astronomical and other calculations had become excessive , and ...
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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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Seite 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...
Seite 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.