Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 pages |
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Page vi
... subtraction of quantities , and the most simple operations belonging to equations of the first degree . The ancients , who had not a knowledge of algebra , supplied the want of it by reasoning and by the use of proportions , which they ...
... subtraction of quantities , and the most simple operations belonging to equations of the first degree . The ancients , who had not a knowledge of algebra , supplied the want of it by reasoning and by the use of proportions , which they ...
Page ix
... subtracted from that represented by A. X signifies multiplied by . Ax B indicates the product arising from the magnitude repre- sented by A being multiplied by the magnitude represented by B , or A multiplied by B. This product is also ...
... subtracted from that represented by A. X signifies multiplied by . Ax B indicates the product arising from the magnitude repre- sented by A being multiplied by the magnitude represented by B , or A multiplied by B. This product is also ...
Page xi
... subtract the antecedent , and compare the difference with the antecedent , this last will be contained once less than it was in the first consequent ; the new ratio then will be equal to the primitive ratio diminished by unity . If the ...
... subtract the antecedent , and compare the difference with the antecedent , this last will be contained once less than it was in the first consequent ; the new ratio then will be equal to the primitive ratio diminished by unity . If the ...
Page 18
... subtracting the sum of these angles from two right angles . 74. Corollary II . If two angles of one triangle are equal to two angles of another triangle , each to each , the third of the one will be equal to the third of the other , and ...
... subtracting the sum of these angles from two right angles . 74. Corollary II . If two angles of one triangle are equal to two angles of another triangle , each to each , the third of the one will be equal to the third of the other , and ...
Page 49
... subtract them from the whole figure --2 --2 ABILKEA , which has for its value AB + BC , it is evident , that there will remain the square ACDE ; therefore , if the line AC , & c . 183. Scholium . This proposition answers to the ...
... subtract them from the whole figure --2 --2 ABILKEA , which has for its value AB + BC , it is evident , that there will remain the square ACDE ; therefore , if the line AC , & c . 183. Scholium . This proposition answers to the ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...