Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and Geometry, in Their Relations and UsesOrr and Smith, 1836 - 496 σελίδες |
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Σελίδα 57
... equal to that in both factors . As our present object is not to teach the practice of arith- metic , but to explain the simplest elementary principles , and to explain these only so far as that the advantage of the scale of numbers in ...
... equal to that in both factors . As our present object is not to teach the practice of arith- metic , but to explain the simplest elementary principles , and to explain these only so far as that the advantage of the scale of numbers in ...
Σελίδα 75
... equal to twice b . But a is the same in both expressions , and there- fore it does not affect the difference , so we may leave it out in both ; and we have this general expression : the difference which the same quantity with the sign + ...
... equal to twice b . But a is the same in both expressions , and there- fore it does not affect the difference , so we may leave it out in both ; and we have this general expression : the difference which the same quantity with the sign + ...
Σελίδα 91
... equal quantities are equal , equal additions are equal , equal subtractions are equal , equal mul- tiplications are equal , and equal divisions are equal ; and therefore we may generalise them all into this one statement , the truth of ...
... equal quantities are equal , equal additions are equal , equal subtractions are equal , equal mul- tiplications are equal , and equal divisions are equal ; and therefore we may generalise them all into this one statement , the truth of ...
Σελίδα 93
... equal to the less quantity , or , the less quantity is equal to half the difference . half the sum We may state the problem formally thus . Give the sum and difference of two quantities to find the quantities themselves ; and the answer ...
... equal to the less quantity , or , the less quantity is equal to half the difference . half the sum We may state the problem formally thus . Give the sum and difference of two quantities to find the quantities themselves ; and the answer ...
Σελίδα 94
... equals , b - f , we have d - g70 , that is , the difference of the differences ; and this will be greater than 0 , equal to it , or less , according as d is greater than g , equal to it , or less . Thirdly , if we add the less to the ...
... equals , b - f , we have d - g70 , that is , the difference of the differences ; and this will be greater than 0 , equal to it , or less , according as d is greater than g , equal to it , or less . Thirdly , if we add the less to the ...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... Robert Mudie Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles Algebra answering apply bisects called centre circle circumference co-efficients compound quantity consequently considered contain cube root denominator diameter difference direction divide dividend division divisor doctrine drawn equi-multiples Euclid's Elements evident exactly equal exponent expressed factors follows four fraction geometrical given greater hypotenuse inclination instance integer number interior angles kind least common multiple less letters line CD logarithm magnitude mathematical means measure meet metical multiplicand multiplier natural numbers necessary number of figures obtained operation opposite parallel parallelogram performed perpendicular plane portion position principle proportion quotient radius ratio re-entering angle reciprocal rectangle relation remaining right angles round a point RULE OF THREE salient angle scale of numbers second term segment side simple solid square root stand straight line subtraction surface taken third tion triangle truth whole
Δημοφιλή αποσπάσματα
Σελίδα 376 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.
Σελίδα 453 - Prove it. 6.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 396 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 360 - If two angles of a triangle are equal, the sides opposite those angles are equal. AA . . A Given the triangle ABC, in which angle B equals angle C. To prove that AB = A C. Proof. 1. Construct the AA'B'C' congruent to A ABC, by making B'C' = BC, Zfi' = ZB, and Z C
Σελίδα 100 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 474 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 136 - Generalising this operation, we have the common rule for finding the greatest common measure of any two numbers : — divide the greater by the less, and the divisor by the remainder continually till nothing remains, and the last divisor is the greatest common measure.
Σελίδα 243 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
Σελίδα 469 - But let one of them BD pass through the centre, and cut the other AC, which does not pass through the centre, at right angles, in the...
Σελίδα 100 - COR. 1. Hence, because AD is the sum, and AC the difference of ' the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square ' of the sum of the lines." " COR. 2. From the demonstration it is manifest, that since the square ' of CD is quadruple of the square of CB, the square of any line is qua' druple of the square of half that line.