Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
Dentro del libro
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Página 22
... greater than AC ( I. 13. ) ; and since AD is equal to AB and BD , or to AB and BC , the two sides AB and A BC are together greater than the third side AC . PROP . XV . THEOR . The difference between two 22 ELEMENTS OF GEOMETRY .
... greater than AC ( I. 13. ) ; and since AD is equal to AB and BD , or to AB and BC , the two sides AB and A BC are together greater than the third side AC . PROP . XV . THEOR . The difference between two 22 ELEMENTS OF GEOMETRY .
Página 23
... difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remainder EC is less than the third side BC . For the two sides AB and BC are ...
... difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remainder EC is less than the third side BC . For the two sides AB and BC are ...
Página 51
... difference between given figures . The smaller rhomboid is here placed below the summit of the other , leaving the defect standing on the original base . PROP . IX . THEOR . A trapezoid is equivalent to the rectangle con- tained by its ...
... difference between given figures . The smaller rhomboid is here placed below the summit of the other , leaving the defect standing on the original base . PROP . IX . THEOR . A trapezoid is equivalent to the rectangle con- tained by its ...
Página 55
... difference between two given squares . Let A and B be the sides of two squares ; it is required to find a square equivalent to their difference . Draw CD equal to the smaller line B , from its extre- mity erect ( I. 34. ) the indefinite ...
... difference between two given squares . Let A and B be the sides of two squares ; it is required to find a square equivalent to their difference . Draw CD equal to the smaller line B , from its extre- mity erect ( I. 34. ) the indefinite ...
Página 57
... difference of two straight lines , is equivalent to the squares of those . lines , diminished by twice their rectangle . Let AC be the difference of two straight lines AB and BC ; the square of AC is equivalent to the excess of the two ...
... difference of two straight lines , is equivalent to the squares of those . lines , diminished by twice their rectangle . Let AC be the difference of two straight lines AB and BC ; the square of AC is equivalent to the excess of the two ...
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Otras ediciones - Ver todas
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.