Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very Copious Notes and IllustrationsW. & C. Tait, and Longman, Hurst, Rees, Orme, & Brown, London, 1820 - 465 páginas |
Dentro del libro
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Página 1
... observation which is termed Experiment . But Geometry takes a more limited view ; and , selecting only the generic property of Magnitude , it can safely pursue the most lengthened train of investigation , and arrive with perfect ...
... observation which is termed Experiment . But Geometry takes a more limited view ; and , selecting only the generic property of Magnitude , it can safely pursue the most lengthened train of investigation , and arrive with perfect ...
Página 2
... observation ; but such observation is so familiar and obvious , that the primary notions which it furnishes might seem intuitive , and have often been regarded as innate . This science , proceed- ing from a basis of extreme simplicity ...
... observation ; but such observation is so familiar and obvious , that the primary notions which it furnishes might seem intuitive , and have often been regarded as innate . This science , proceed- ing from a basis of extreme simplicity ...
Página 198
... observed , that these radii mutually ap proximate about four times nearer at each step : For , ( II . 10. ) CA2 = OA2 — OC2 = ( II . 17. ) ( OA — OC ) ( OA + OC ) ; and , for the same reason , GE DE'— DG2 = ( DE — DG ) ( DE + DG ) . But ...
... observed , that these radii mutually ap proximate about four times nearer at each step : For , ( II . 10. ) CA2 = OA2 — OC2 = ( II . 17. ) ( OA — OC ) ( OA + OC ) ; and , for the same reason , GE DE'— DG2 = ( DE — DG ) ( DE + DG ) . But ...
Página 230
... entire circumferences . Hence the sine of an arc a is the same with the sine of any arc n.360 ° + a . It may be farther observed , that the tangent of any arc ending at B is the same as the tangent of 230 ELEMENTS OF.
... entire circumferences . Hence the sine of an arc a is the same with the sine of any arc n.360 ° + a . It may be farther observed , that the tangent of any arc ending at B is the same as the tangent of 230 ELEMENTS OF.
Página 263
... observed , that the cosines of an angle and of its supple- ment are the same , only placed in opposite directions ; and hence the second term of the analogy , or the differ- ence of AB + BC from AC , is in excess or defect , ac- cording ...
... observed , that the cosines of an angle and of its supple- ment are the same , only placed in opposite directions ; and hence the second term of the analogy , or the differ- ence of AB + BC from AC , is in excess or defect , ac- cording ...
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Otras ediciones - Ver todas
Elements of Geometry and Plane Trigonometry. with an Appendix, and Copious ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Copious ... John Leslie,University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2017 |
Términos y frases comunes
ABCD adjacent angle altitude angle ABC angle ACB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle corresponding cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC evidently expressed exterior angle Geometry given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise mean proportional measure multiple parallel perpendicular point G polygon PROB PROP proposition quadrant quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sexagesimal side AC sine square of AB square of AC straight line tangent THEOR tion toises triangle ABC Trigonometry twice the rectangle twice the square vertex vertical angle whence Wherefore
Pasajes populares
Página 110 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 30 - 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.
Página 334 - the first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Página 293 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Página 88 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Página 295 - 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...
Página 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 129 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Página 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.