A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 σελίδες |
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Σελίδα xi
... taken effectively . Algebra , a method of performing the calculations of all kinds of quantities by means of general signs or characters . Aliquot part , such a part of a number as will exactly divide it with- out a remainder ...
... taken effectively . Algebra , a method of performing the calculations of all kinds of quantities by means of general signs or characters . Aliquot part , such a part of a number as will exactly divide it with- out a remainder ...
Σελίδα xvi
... taken as often as there are terms in the progression . Cavalleri showed , that when the number of terms is infinitely great , the first of these sums is just one - third of the second ; which led to the cubature of many solids . He then ...
... taken as often as there are terms in the progression . Cavalleri showed , that when the number of terms is infinitely great , the first of these sums is just one - third of the second ; which led to the cubature of many solids . He then ...
Σελίδα xvi
... taken two and two ; the same taken three and three , & c . whether the roots be positive or negative . He appears also to have been the first who understood the use of negative roots in the solution of geometrical problems , and is the ...
... taken two and two ; the same taken three and three , & c . whether the roots be positive or negative . He appears also to have been the first who understood the use of negative roots in the solution of geometrical problems , and is the ...
Σελίδα xix
... taken by the two inventors were not precisely the same . Leibnitz , considering the differences of the variable quantities as infinitely small , conceived that he might reject the higher powers of those differences without any sensible ...
... taken by the two inventors were not precisely the same . Leibnitz , considering the differences of the variable quantities as infinitely small , conceived that he might reject the higher powers of those differences without any sensible ...
Σελίδα xxii
... taken up into the atmosphere , to maintain the perennial flow of springs and rivers , was established by undeniable evidence . The difficulty which men found in conceiving how a precarious and accidental supply like that of the rains ...
... taken up into the atmosphere , to maintain the perennial flow of springs and rivers , was established by undeniable evidence . The difficulty which men found in conceiving how a precarious and accidental supply like that of the rains ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Σελίδα 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...
Σελίδα 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.