Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
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Page xiii
... common elements , and received the appellation of the higher or sublime geometry . The important addition of conic sections to the mathematical sciences being , as before observed , particularly cultivated by the geometers of that time ...
... common elements , and received the appellation of the higher or sublime geometry . The important addition of conic sections to the mathematical sciences being , as before observed , particularly cultivated by the geometers of that time ...
Page 8
... common angle FAG . fore the base rc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ...
... common angle FAG . fore the base rc is equal to the base GB , and the tri- angle AFC equal to the triangle AGB also the remain- ing angles shall be equal to the remaining angles , each to each , viz . , the angle ACF equal to the angle ...
Page 9
... common , the two DB , BC , will be equal to the two AC , CB , each to each ; and the angle DBC equal to the angle ACB ( by hypoth . ) . Whence the base Dc is equal to 4.1 . to the base AB , and the triangle DBC equal to the triangle ACB ...
... common , the two DB , BC , will be equal to the two AC , CB , each to each ; and the angle DBC equal to the angle ACB ( by hypoth . ) . Whence the base Dc is equal to 4.1 . to the base AB , and the triangle DBC equal to the triangle ACB ...
Page 12
... common : the two DA , AF , are equal to the two EA , AF , each to each ; and the base DF is equal to the base EF : therefore the angle DAF is equal to the angle EAF . Wherefore the given rectilineal angle BAC is bisected by the right ...
... common : the two DA , AF , are equal to the two EA , AF , each to each ; and the base DF is equal to the base EF : therefore the angle DAF is equal to the angle EAF . Wherefore the given rectilineal angle BAC is bisected by the right ...
Page 13
... common ; the two DC , CF , will be equal to the two EC , CF , each to each ; and the base DF is equal to the base EF ; wherefore the angle DCF is equal to the angle ECF , and they are adjacent angles . But when a right line standing ...
... common ; the two DC , CF , will be equal to the two EC , CF , each to each ; and the base DF is equal to the base EF ; wherefore the angle DCF is equal to the angle ECF , and they are adjacent angles . But when a right line standing ...
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Common terms and phrases
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circum circumference BC diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth Geometry given circle given point given right line gnomon greater ratio hence inscribed join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deduction Q. E. D. PROPOSITION rectangle contained remaining angle right angles right line AB right line AC sector HEF segment side BC similar and similarly square of AC subtending THEOREM tiple touches the circle triangle ABC triangle DEF whence whole
Popular passages
Page xxvi - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 148 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Page 8 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Page 73 - DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Page 99 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Page 7 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Page 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.