Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 sider |
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Side ix
... less distinguished than the former for the variety and extent of his discoveries ; among the most eminent of these , at least in Geometry , which he made , may be mentioned , that the square of the hypothenuse of a right angled triangle ...
... less distinguished than the former for the variety and extent of his discoveries ; among the most eminent of these , at least in Geometry , which he made , may be mentioned , that the square of the hypothenuse of a right angled triangle ...
Side xvii
... perimeters of the in- scribed and circumscribed polygons ; from which calculation it appears , that the perimeter of the circumscribed regular polygon of 192 sides is to b its diameter in a less ratio than 34 to 1 INTRODUCTION . xvii.
... perimeters of the in- scribed and circumscribed polygons ; from which calculation it appears , that the perimeter of the circumscribed regular polygon of 192 sides is to b its diameter in a less ratio than 34 to 1 INTRODUCTION . xvii.
Side xviii
Euclid. its diameter in a less ratio than 34 to 1 , and that the perimeter of the inscribed polygon of 96 sides is to the diameter in a greater ratio than that of 3 to 1 : therefore the ratio of the circumference to its diameter must be ...
Euclid. its diameter in a less ratio than 34 to 1 , and that the perimeter of the inscribed polygon of 96 sides is to the diameter in a greater ratio than that of 3 to 1 : therefore the ratio of the circumference to its diameter must be ...
Side xxii
... less eminent than they were numerous . Amongst whom was the much esteemed Synesius , afterward bishop of Ptolemais . But it was not Synesius only , and the disciples of the Alexandrian School , who admired Hypatia for her virtue and ...
... less eminent than they were numerous . Amongst whom was the much esteemed Synesius , afterward bishop of Ptolemais . But it was not Synesius only , and the disciples of the Alexandrian School , who admired Hypatia for her virtue and ...
Side xxviii
... the Work . + is the sign of Addition . ÷ + 1 × · | · || ^ V : Subtraction . Multiplication . Division . Equality . > signifies greater than . ... less than . therefore . EUCLID'S ELEMENTS . BOOK I. DEFINITIONS . 1. A POINT.
... the Work . + is the sign of Addition . ÷ + 1 × · | · || ^ V : Subtraction . Multiplication . Division . Equality . > signifies greater than . ... less than . therefore . EUCLID'S ELEMENTS . BOOK I. DEFINITIONS . 1. A POINT.
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.