Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 páginas |
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Página 2
... three dimen- sions of length , breadth , and thickness . A The uniform description of a line which through its whole extent stretches in the same direction gives the idea of a straight line . Hence , 2 ELEMENTS OF GEOMETRY .
... three dimen- sions of length , breadth , and thickness . A The uniform description of a line which through its whole extent stretches in the same direction gives the idea of a straight line . Hence , 2 ELEMENTS OF GEOMETRY .
Página 24
... is ( I. 8. ) equal to BHA , and therefore the two angles IBH and HBA are greater than IHB and BHA , that is , the whole angle CBA is greater than IHA or GHA . And since the sides of the triangle 7 . 24 ELEMENTS OF GEOMETRY . B ...
... is ( I. 8. ) equal to BHA , and therefore the two angles IBH and HBA are greater than IHB and BHA , that is , the whole angle CBA is greater than IHA or GHA . And since the sides of the triangle 7 . 24 ELEMENTS OF GEOMETRY . B ...
Página 34
... whole exterior angle BCD . Add the adjacent angle BCA to each ; and all the interior angles of the triangle ABC are together equal to the angles BCD and A D BCA on the same side of the straight line AD , that is , to two right angles ...
... whole exterior angle BCD . Add the adjacent angle BCA to each ; and all the interior angles of the triangle ABC are together equal to the angles BCD and A D BCA on the same side of the straight line AD , that is , to two right angles ...
Página 35
... whole amount there is to be deducted the vertical angles about the point O , and which are ( Def . 4. ) equal to four right angles . Cor . Hence all the angles of a quadrilateral figure are equal to four right angles , those of a ...
... whole amount there is to be deducted the vertical angles about the point O , and which are ( Def . 4. ) equal to four right angles . Cor . Hence all the angles of a quadrilateral figure are equal to four right angles , those of a ...
Página 38
... whole angle FBC must be an entire right angle , or the straight line BF is perpendicular to AB . PROP . XXXIX . PROB . On a given finite straight line to construct a square . Let AB be the side of the square which it is required to ...
... whole angle FBC must be an entire right angle , or the straight line BF is perpendicular to AB . PROP . XXXIX . PROB . On a given finite straight line to construct a square . Let AB be the side of the square which it is required to ...
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Términos y frases comunes
ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines draw drawn equal to BC evidently exterior angle fall the perpendicular given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall likewise mean proportional parallel perpendicular point F polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AC squares of AB tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Pasajes populares
Página 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Página 28 - ... 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 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 34 - 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 153 - 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 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Página 411 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página 58 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.
Página 64 - 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...
Página 157 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.