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 2
... given by the Alexandrian geometer ; and during this long period , men of all ranks , from the monarch to the peasant , have studied and promoted geometry , and the other branches of mathematical science ; but this reply has been brought ...
... given by the Alexandrian geometer ; and during this long period , men of all ranks , from the monarch to the peasant , have studied and promoted geometry , and the other branches of mathematical science ; but this reply has been brought ...
Σελίδα 7
... given , for this simple reason , that no truth can be regarded as such until it is known to be so . When no proof has been given , but there is still some pro- bability that a position may be true , it is a proposition , or hypo- thesis ...
... given , for this simple reason , that no truth can be regarded as such until it is known to be so . When no proof has been given , but there is still some pro- bability that a position may be true , it is a proposition , or hypo- thesis ...
Σελίδα 42
... given ; and the same in all other cases . It is not necessary , however , that the given quantity should be in the same denomination with that which is sought , provided we know the relation between them . For instance , if a certain ...
... given ; and the same in all other cases . It is not necessary , however , that the given quantity should be in the same denomination with that which is sought , provided we know the relation between them . For instance , if a certain ...
Σελίδα 44
... given ones would make a sum equal to the greater , or which taken away from the greater would leave a remainder equal to the less . The process by which we find a sum is called ADDITION , and that by which we find a difference is called ...
... given ones would make a sum equal to the greater , or which taken away from the greater would leave a remainder equal to the less . The process by which we find a sum is called ADDITION , and that by which we find a difference is called ...
Σελίδα 45
... given quantities , and therefore it must be greater or less according as they , taken in their whole amount , are greater or less ; whereas the result of a subtraction expresses merely the difference of the quantities , and thus it has ...
... given quantities , and therefore it must be greater or less according as they , taken in their whole amount , are greater or less ; whereas the result of a subtraction expresses merely the difference of the quantities , and thus it has ...
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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.