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 xvi
... PLANE FIGURES , THEIR BOUNDING LINES , THE ANGLES MADE BY THOSE LINES , LINES INTER- SECTING THEM , AND THEIR SURFACES OR AREAS 411 General Maxim 412 Triangles Parallelograms , Rectangles , and Squares Similar Figures Lines and Circles ...
... PLANE FIGURES , THEIR BOUNDING LINES , THE ANGLES MADE BY THOSE LINES , LINES INTER- SECTING THEM , AND THEIR SURFACES OR AREAS 411 General Maxim 412 Triangles Parallelograms , Rectangles , and Squares Similar Figures Lines and Circles ...
Σελίδα 177
... plane will touch all the four crosses , or branches formed by the crossing , as far as their arms and the plane extend : also , if two planes touch each other in three points , they will touch each other in every point , as far as they ...
... plane will touch all the four crosses , or branches formed by the crossing , as far as their arms and the plane extend : also , if two planes touch each other in three points , they will touch each other in every point , as far as they ...
Σελίδα 180
... plane , from the very nature of a straight line and a plane ; and it follows from this , that two straight lines which have the same direction must be in the same plane , and this brings us a little nearer to the definition , and would ...
... plane , from the very nature of a straight line and a plane ; and it follows from this , that two straight lines which have the same direction must be in the same plane , and this brings us a little nearer to the definition , and would ...
Σελίδα 182
... plane , and that they cannot meet in two points , however near or however far asunder these points may be , without coinciding altogether , or being one and the same . Now straight lines which are in the same plane must either , if con ...
... plane , and that they cannot meet in two points , however near or however far asunder these points may be , without coinciding altogether , or being one and the same . Now straight lines which are in the same plane must either , if con ...
Σελίδα 184
... plane . We may therefore assume it as a necessary conclusion , from the very nature of straight lines , from the fact that every straight line lies wholly in one unchangeable direc- tion to whatever length it may be continued , that if ...
... plane . We may therefore assume it as a necessary conclusion , from the very nature of straight lines , from the fact that every straight line lies wholly in one unchangeable direc- tion to whatever length it may be continued , that if ...
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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 angular space answering apply bisects breadth called centre circle circumference co-efficients compound quantity consequently considered consists contain cube root decimal point denominator diameter difference direction divide dividend division divisor drawn equi-multiples Euclid's Elements evident exactly equal exponent expressed factors follows four fraction geometrical geometrical series greater hypotenuse inclination instance integer number interior angles kind least common multiple length less letters logarithm magnitude mathematical means measure meet metical multiplicand multiplier natural numbers necessary number of figures obtained operation opposite parallel parallelogram performed perpendicular plane position principle proportion quan quotient radius ratio reciprocal rectangle relation remaining right angles round a point salient angle scale of numbers second term segment sides simple solid space round square root stand straight line subtraction surface taken third tion triangle truth whole
Δημοφιλή αποσπάσματα
Σελίδα 396 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.
Σελίδα 473 - 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 416 - 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 380 - 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 494 - 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 138 - 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 259 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
Σελίδα 489 - 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 102 - 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.