Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 Seiten |
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... a line , abstract- ing its continuity , leaves nothing in the imagina- tion but the points which form its extremities . solid is bounded by surfaces ; a surface is circum- scribed by lines ; and a line is terminated by points . A point ...
... a line , abstract- ing its continuity , leaves nothing in the imagina- tion but the points which form its extremities . solid is bounded by surfaces ; a surface is circum- scribed by lines ; and a line is terminated by points . A point ...
Seite 12
... point A being laid on D , and the side AC on DE , their other extremities C and E must coin- cide , since AC is equal to DE . And because AB is equal to DF , the point B must be found in the circumference of a circle de- scribed from D ...
... point A being laid on D , and the side AC on DE , their other extremities C and E must coin- cide , since AC is equal to DE . And because AB is equal to DF , the point B must be found in the circumference of a circle de- scribed from D ...
Seite 13
... a point in a straight line , to make an angle equal to a given angle . At the point D in the given straight line DE to form an angle equal to the given angle BAC . In the sides AB and AC of the given angle , assume the points G and H ...
... a point in a straight line , to make an angle equal to a given angle . At the point D in the given straight line DE to form an angle equal to the given angle BAC . In the sides AB and AC of the given angle , assume the points G and H ...
Seite 14
... a given angle . H Let ABC be an angle which it is required to bisect . In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct the isosceles triangle DEF ( I. 1. ) , and draw the straight line ...
... a given angle . H Let ABC be an angle which it is required to bisect . In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct the isosceles triangle DEF ( I. 1. ) , and draw the straight line ...
Seite 15
... a perpendicular upon a straight line , from a given point without it . From the point C to let fall a perpendicular upon a given straight line AB . In AB take the point D , and with the distance DC de- scribe a circle ; and in the same line ...
... a perpendicular upon a straight line , from a given point without it . From the point C to let fall a perpendicular upon a given straight line AB . In AB take the point D , and with the distance DC de- scribe a circle ; and in the same line ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Seite 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.
Seite 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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...
Seite 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.