Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 Seiten |
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Seite 18
... ACB is greater than the interior and opposite angle ABC ; add ACB , which is common . There- fore the angles ACD , ACB , are greater than the angles ABC , ACB . But ACD , ACB , are equal to two right angles , whence ABC , BCA , are less ...
... ACB is greater than the interior and opposite angle ABC ; add ACB , which is common . There- fore the angles ACD , ACB , are greater than the angles ABC , ACB . But ACD , ACB , are equal to two right angles , whence ABC , BCA , are less ...
Seite 29
... angle equal to a given rectilineal angle . 2. From a given isosceles triangle to cut off a trape- zium , which shall ... ACB , which is common : therefore the angles ACD , ACB , B D D A E * The three angles of a triangle may be ...
... angle equal to a given rectilineal angle . 2. From a given isosceles triangle to cut off a trape- zium , which shall ... ACB , which is common : therefore the angles ACD , ACB , B D D A E * The three angles of a triangle may be ...
Seite 30
... ACB , are equal to two right angles.c Therefore the angles ACB , CBA , CAB , will also be equal to two right angles . Therefore if one side of every triangle , & c . Q. E. D. Deductions . 1. The angle ... angle and two right angles . 2. The ...
... ACB , are equal to two right angles.c Therefore the angles ACB , CBA , CAB , will also be equal to two right angles . Therefore if one side of every triangle , & c . Q. E. D. Deductions . 1. The angle ... angle and two right angles . 2. The ...
Seite 31
... angle ACB is equal to the angle CBD . And because the right line BC falls upon the two right lines AC , BD , makes the alternate angles ACB , CBD , equal to one another , AC с is parallel to BD . But it was shown that it was equal © 27 ...
... angle ACB is equal to the angle CBD . And because the right line BC falls upon the two right lines AC , BD , makes the alternate angles ACB , CBD , equal to one another , AC с is parallel to BD . But it was shown that it was equal © 27 ...
Seite 68
... angles ; therefore FEB is a right angle . But FEA was shown to be a right angle . Wherefore the angle FEA will be ... ACB in F. Be- cause E is the centre of the circle ABC , EC will be equal to EF , and because E is the centre of the ...
... angles ; therefore FEB is a right angle . But FEA was shown to be a right angle . Wherefore the angle FEA will be ... ACB in F. Be- cause E is the centre of the circle ABC , EC will be equal to EF , and because E is the centre of the ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
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.