Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 páginas |
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Página 11
... c . Q. E. D. Deduction from Euclid . In an isosceles triangle , the right line drawn from the vertical angle bisecting the base is at right angles to the base . a 3. 1 . b 1.1 . с c 8. PROP . 8. ] 11 EUCLID'S ELEMENTS .
... c . Q. E. D. Deduction from Euclid . In an isosceles triangle , the right line drawn from the vertical angle bisecting the base is at right angles to the base . a 3. 1 . b 1.1 . с c 8. PROP . 8. ] 11 EUCLID'S ELEMENTS .
Página 12
... bisect a given finite right line , that is , to divide it into two equal parts . Let AB be the given finite right line ; it is required to bisect it . Upon ita describe the equilateral triangle ABC ; and bisect the angle ACB by the ...
... bisect a given finite right line , that is , to divide it into two equal parts . Let AB be the given finite right line ; it is required to bisect it . Upon ita describe the equilateral triangle ABC ; and bisect the angle ACB by the ...
Página 14
... bisect GE in H ; and join CG , CH , CE . cular CH is drawn upon the given infinite right line ab from the point c , which is without it . b H D E B The perpendi- For because GH is equal to HE , and HC common , the two GH , HC , are ...
... bisect GE in H ; and join CG , CH , CE . cular CH is drawn upon the given infinite right line ab from the point c , which is without it . b H D E B The perpendi- For because GH is equal to HE , and HC common , the two GH , HC , are ...
Página 17
... Bisect Ac in E , and BE being joined , produce it to F , and make EF equal to BE ; join also Fc , and produce Ac to G. Therefore because A E is equal to Ec , and BE to EF , the two AE , EB , are equal to the two CE , EF , each to each ...
... Bisect Ac in E , and BE being joined , produce it to F , and make EF equal to BE ; join also Fc , and produce Ac to G. Therefore because A E is equal to Ec , and BE to EF , the two AE , EB , are equal to the two CE , EF , each to each ...
Página 19
... third side . 2. Two sides of a triangle are together greater than twice the line from the vertex bisecting the base . с a 20. 1 . b Ax . 4 . 16. c 2 PROP . 20. ] 19 EUCLID'S ELEMENTS . fore AC is not less than AB. And it ...
... third side . 2. Two sides of a triangle are together greater than twice the line from the vertex bisecting the base . с a 20. 1 . b Ax . 4 . 16. c 2 PROP . 20. ] 19 EUCLID'S ELEMENTS . fore AC is not less than AB. And it ...
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Elements of Geometry; Containing the First Six Books of Euclid ... Euclid,John Playfair Vista completa - 1814 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.