Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 Seiten |
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Seite 7
... angle BAC equal to the angle EDF . Then is the base AA BC equal to the base EF , and the triangle ABC equal to the triangle DEF ; also the remaining angles equal to the remaining angles , R each to each , to which the equal CE sides are ...
... angle BAC equal to the angle EDF . Then is the base AA BC equal to the base EF , and the triangle ABC equal to the triangle DEF ; also the remaining angles equal to the remaining angles , R each to each , to which the equal CE sides are ...
Seite 11
... angle BAC equal to the angle EDF . For the tri- angle ABC being applied to the triangle DEF , and the point B being put on E ; also the right line BC being applied to EF , the point c will coincide with A Да B CE F the point F , because ...
... angle BAC equal to the angle EDF . For the tri- angle ABC being applied to the triangle DEF , and the point B being put on E ; also the right line BC being applied to EF , the point c will coincide with A Да B CE F the point F , because ...
Seite 12
... angle , that is , to divide it into two equal parts . D E Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in the right line AB , and from the line AC take AE equal to AD , and DE being joined ...
... angle , that is , to divide it into two equal parts . D E Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in the right line AB , and from the line AC take AE equal to AD , and DE being joined ...
Seite 17
... angles . F a 15. 1 . E b 4. 1 . D Let ABC be a triangle , and let one of its sides BC be produced to D. The exterior angle ACD is greater than either of the interior and opposite angles ; namely , the angles CBA and BAC . Bisect Ac in E ...
... angles . F a 15. 1 . E b 4. 1 . D Let ABC be a triangle , and let one of its sides BC be produced to D. The exterior angle ACD is greater than either of the interior and opposite angles ; namely , the angles CBA and BAC . Bisect Ac in E ...
Seite 18
... angle ABC ; add ACB , which is common . There- fore the angles ACD , ACB , are greater than the angles ABC , ACB ... BAC , ACB , and also CAB , ABC , are less than two right angles . Therefore two angles of every triangle , & c . Q. E. D. ...
... angle ABC ; add ACB , which is common . There- fore the angles ACD , ACB , are greater than the angles ABC , ACB ... BAC , ACB , and also CAB , ABC , are less than two right angles . Therefore two angles of every triangle , & c . Q. E. D. ...
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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
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Seite 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.
Seite 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.