Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
From inside the book
Results 1-5 of 86
Page iii
... measures in the questions , where it was thought neces- sary . When there has been an occasion to add a note by way of illustration , the reference is made by a letter or an obelisk , the author's being always distinguished by an ...
... measures in the questions , where it was thought neces- sary . When there has been an occasion to add a note by way of illustration , the reference is made by a letter or an obelisk , the author's being always distinguished by an ...
Page 31
... measure respectively the areas of the surfaces and the bulks of bodies , the former of which have two and the latter three dimensions ; but beyond this limit the correspond- ence between the algebraic expressions and geometrical figures ...
... measure respectively the areas of the surfaces and the bulks of bodies , the former of which have two and the latter three dimensions ; but beyond this limit the correspond- ence between the algebraic expressions and geometrical figures ...
Page 84
... measures of rye , 20 of barley , and 10 of wheat , cost 230 francs ; The second , which contained 15 measures of rye , 6 of barley , and 12 of wheat , cost 138 francs ; A The third , which contained 10 measures of rye 84 Elements of Algebra ...
... measures of rye , 20 of barley , and 10 of wheat , cost 230 francs ; The second , which contained 15 measures of rye , 6 of barley , and 12 of wheat , cost 138 francs ; A The third , which contained 10 measures of rye 84 Elements of Algebra ...
Page 85
... measure ? Let a be the price of a measure of rye , that of a measure of barley , y , z , that of a measure of wheat . To fulfil the first condition , we observe , that 30 measures of rye are worth 30x , 20 measures of barley are worth ...
... measure ? Let a be the price of a measure of rye , that of a measure of barley , y , z , that of a measure of wheat . To fulfil the first condition , we observe , that 30 measures of rye are worth 30x , 20 measures of barley are worth ...
Page 86
... measure was 4 fr . , that of the barley that of the wheat 3 , 5 . This example , while it illustrates the method given in the pre- ceding article , ought to be attended to , on account of the abbre- viations of calculation , which are ...
... measure was 4 fr . , that of the barley that of the wheat 3 , 5 . This example , while it illustrates the method given in the pre- ceding article , ought to be attended to , on account of the abbre- viations of calculation , which are ...
Contents
1 | |
2 | |
8 | |
14 | |
23 | |
30 | |
46 | |
53 | |
160 | |
168 | |
170 | |
174 | |
180 | |
186 | |
190 | |
192 | |
59 | |
66 | |
81 | |
91 | |
98 | |
99 | |
105 | |
111 | |
117 | |
123 | |
131 | |
136 | |
149 | |
150 | |
13 | |
27 | |
36 | |
8 | |
22 | |
44 | |
77 | |
86 | |
220 | |
Other editions - View all
Common terms and phrases
a² b³ algebraic Algebraic Quantities Arith arithmetic becomes binomial changing the signs coefficient common divisor consequently contains courier cube root decimal deduce denominator denoted divided dividend division employed entire number enunciation equa evident example exponent expression extract the root figures follows formula fraction given in art given number gives greater greatest common divisor last term letters logarithm manner method multiplicand multiplied negative number of arrangements observed obtain operation perfect square polynomials preceding article proposed equation proposed number quan question quotient radical quantities radical sign reduced remainder represented resolve result rule given second degree second member second term simple quantities square root subtract suppose taken tens third tion tities units unity unknown quantity vulgar fractions whence whole numbers
Popular passages
Page 9 - 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 44 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 101 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 122 - ... is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots.
Page 180 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Page 54 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 185 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Page 164 - 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.