Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
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Página 1
... hence directed by that refined spe- cies of 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 ...
... hence directed by that refined spe- cies of 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 ...
Página 16
... Hence the mode of drawing a perpendicular from a given point B in the straight line AC ; for the angle ABC , which the opposite seg- F ments BA and BC make with each other , being equal to two right angles , the straight line that ...
... Hence the mode of drawing a perpendicular from a given point B in the straight line AC ; for the angle ABC , which the opposite seg- F ments BA and BC make with each other , being equal to two right angles , the straight line that ...
Página 19
... hence BCF must be greater than either the angle CBA or CAB . Cor . Hence all the exterior angles of a triangle are greater than the interior , and likewise greater than three right angles . PROP . IX . THEOR . Any two angles of a ...
... hence BCF must be greater than either the angle CBA or CAB . Cor . Hence all the exterior angles of a triangle are greater than the interior , and likewise greater than three right angles . PROP . IX . THEOR . Any two angles of a ...
Página 25
... Hence only a single perpendicular CD can be let fall from the same point C upon a given straight line AB ; and hence also a pair only of equal straight lines greater than CD can at once be extended from C to AB , making on the same side ...
... Hence only a single perpendicular CD can be let fall from the same point C upon a given straight line AB ; and hence also a pair only of equal straight lines greater than CD can at once be extended from C to AB , making on the same side ...
Página 26
... hence still greater than BCA or BCH ; consequently the side BC or EF is ( I. 13. ) greater than BH . In every case , therefore , the point G must lie below the base AC . But the triangle GBC being evidently isosceles , its angles BGC ...
... hence still greater than BCA or BCH ; consequently the side BC or EF is ( I. 13. ) greater than BH . In every case , therefore , the point G must lie below the base AC . But the triangle GBC being evidently isosceles , its angles BGC ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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...
Página 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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.
Página 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.
Página 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
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.
Página 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.