A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for Exercise |
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Σελίδα xvi
scribing another round it , two limits could be ovrained , one greater and the other less than the area required . It was also evident , that , by increasing the number , and diminishing the sides of those figures , the two limits might ...
scribing another round it , two limits could be ovrained , one greater and the other less than the area required . It was also evident , that , by increasing the number , and diminishing the sides of those figures , the two limits might ...
Σελίδα xvi
At first , however , his system attracted little notice , and was rejected by the greater part even of astronomers . fermenting in secret with other new discoveries for more than fifty years , till , by the exertions of Galileo , it was ...
At first , however , his system attracted little notice , and was rejected by the greater part even of astronomers . fermenting in secret with other new discoveries for more than fifty years , till , by the exertions of Galileo , it was ...
Σελίδα 4
From the greater of these sums subtract the less , and to the remainder prefix the sign of the greater , and annex the common letters . Note .-- If the aggregate of the positive terms equal to that of the Degative ones , their sums will ...
From the greater of these sums subtract the less , and to the remainder prefix the sign of the greater , and annex the common letters . Note .-- If the aggregate of the positive terms equal to that of the Degative ones , their sums will ...
Σελίδα 31
Obs . As their difference is 12 , the greater aamber must evidently exceed the less pumber by 12 . Solu . Let x = the less number ; then x + 12 will be the greater But by the equation , the sum of the two numbers is 20 ; or , the ...
Obs . As their difference is 12 , the greater aamber must evidently exceed the less pumber by 12 . Solu . Let x = the less number ; then x + 12 will be the greater But by the equation , the sum of the two numbers is 20 ; or , the ...
Σελίδα 52
X , or 30 7 289 17 Consequently , 1 = + Therefore s = + 17 + 7 = 12 , or -5 = less part ; 2 And x + 7 = 12 + 7 or — 5 +7 19 or 2 = the greater part . Note . This problem , we see , admits of a double solution ; for wbether 12 and 19 or ...
X , or 30 7 289 17 Consequently , 1 = + Therefore s = + 17 + 7 = 12 , or -5 = less part ; 2 And x + 7 = 12 + 7 or — 5 +7 19 or 2 = the greater part . Note . This problem , we see , admits of a double solution ; for wbether 12 and 19 or ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude axis base become called centre circle circumference co-efficient common cone consequently contained convergency curve denominator describe diameter difference distance divided draw drawn equal equation Examples expression factors feet figure fluxion four fraction function given gives greater half Hence infinite integral join less magnitudes manner measure meet meridian method Multiply opposite original parallel parallelogram pass perpendicular plane pole Prob probability Problem projection Prop proportional Proposition pyramid quantity radius ratio rectangle Reduce remaining represented result right angles root rule sides similar sine solid sphere square straight line subtract suppose taken tang tangent Theorem things third triangle vanishing whence Wherefore whole
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.