Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 126
... quantities of the same kind , the one may contain the other , or be contained by it ; that is , the one may result ... quantities are not all suscep- tible of such perfect mensuration . Two quantities may be 126 ELEMENTS OF GEOMETRY .
... quantities of the same kind , the one may contain the other , or be contained by it ; that is , the one may result ... quantities are not all suscep- tible of such perfect mensuration . Two quantities may be 126 ELEMENTS OF GEOMETRY .
Seite 127
... quantities may be conceived to be so constituted , as not to ad- mit of any other quantity that will measure them completely , or be contained in both without leaving a remainder . Yet this apparent imperfection , which proceeds ...
... quantities may be conceived to be so constituted , as not to ad- mit of any other quantity that will measure them completely , or be contained in both without leaving a remainder . Yet this apparent imperfection , which proceeds ...
Seite 128
... Quantities are homogeneous , which can be added to- gether . 2. One quantity is said to contain another , when the subtraction of the smaller - continued if necessary - leaves no remainder . 3. A quantity which is contained in another ...
... Quantities are homogeneous , which can be added to- gether . 2. One quantity is said to contain another , when the subtraction of the smaller - continued if necessary - leaves no remainder . 3. A quantity which is contained in another ...
Seite 129
... quantities are said to be proportional , when a submultiple of the first is contained in the second as often as a like submultiple of the third is contained in the fourth . 11. Of proportional quantities , the first of each pair is ...
... quantities are said to be proportional , when a submultiple of the first is contained in the second as often as a like submultiple of the third is contained in the fourth . 11. Of proportional quantities , the first of each pair is ...
Seite 130
... quantities . " Thus , the ratio of A to D is viewed as compounded of that of A to B , that of B to C , and that of C to D. 19. Of quantities in a continued proportion , the first is said to have to the third , the duplicate ratio of ...
... quantities . " Thus , the ratio of A to D is viewed as compounded of that of A to B , that of B to C , and that of C to D. 19. Of quantities in a continued proportion , the first is said to have to the third , the duplicate ratio of ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
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ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
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Seite 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Seite 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Seite 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Seite 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Seite 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Seite 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Seite 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.