Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and Geometry, in Their Relations and UsesOrr and Smith, 1836 - 496 sider |
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Side 183
... inclination must be the same to what- ever length we may suppose them to be continued either way . Their positions with regard to each other are reversed on opposite sides of the point where they meet and cross each 184 LINES WHICH ARE ...
... inclination must be the same to what- ever length we may suppose them to be continued either way . Their positions with regard to each other are reversed on opposite sides of the point where they meet and cross each 184 LINES WHICH ARE ...
Side 184
... inclination must be everywhere the same in amount . If we view them as from the point where they cross , they must have the same inclination from each other on the one side of this point and on the other ; and if we view them toward the ...
... inclination must be everywhere the same in amount . If we view them as from the point where they cross , they must have the same inclination from each other on the one side of this point and on the other ; and if we view them toward the ...
Side 185
... inclination must be constant , that is , the same at every point of the lines , follows also from the very fact of their being straight , because the inclination could vary only in con- sequence of a change in the direction of one of ...
... inclination must be constant , that is , the same at every point of the lines , follows also from the very fact of their being straight , because the inclination could vary only in con- sequence of a change in the direction of one of ...
Side 186
... , it will be md - md = 0 , that is , the lines will meet . Wherefore , it is not only universally true that two straight lines which are in the same plane , and have an inclination to LINES WHICH MEET . 187 each other must meet if.
... , it will be md - md = 0 , that is , the lines will meet . Wherefore , it is not only universally true that two straight lines which are in the same plane , and have an inclination to LINES WHICH MEET . 187 each other must meet if.
Side 187
... inclination toward each other one way , and from each other the other way , these two lines have exactly the same direction , that is , what- ever can be proved by the direction of one of them will neces- sarily hold good as equally ...
... inclination toward each other one way , and from each other the other way , these two lines have exactly the same direction , that is , what- ever can be proved by the direction of one of them will neces- sarily hold good as equally ...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... Robert Mudie Uten tilgangsbegrensning - 1836 |
Popular Mathematics, being the first elements of arithmetic, algebra and ... Robert Mudie Uten tilgangsbegrensning - 1836 |
Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... Robert Mudie Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 376 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.
Side 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.
Side 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.
Side 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
Side 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.
Side 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.
Side 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.
Side 243 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
Side 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...
Side 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.