Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 Seiten |
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Seite x
... proposition of the same book , viz . that the three angles of any triangle are together equal to two right angles ; as likewise to have shown that only three polygons , or regular plane figures , can fill up the space about a point ...
... proposition of the same book , viz . that the three angles of any triangle are together equal to two right angles ; as likewise to have shown that only three polygons , or regular plane figures , can fill up the space about a point ...
Seite 5
Euclid. PROPOSITION I. PROBLEM . Upon a given finite right line to describe an equilateral triangle Let AB be the given ... PROPOSITION II . PROBLEM . From a given point to draw a right line equal to a given right line . F Let A be the ...
Euclid. PROPOSITION I. PROBLEM . Upon a given finite right line to describe an equilateral triangle Let AB be the given ... PROPOSITION II . PROBLEM . From a given point to draw a right line equal to a given right line . F Let A be the ...
Seite 6
... PROPOSITION III . PROBLEM . Two unequal right lines being given , to cut off from the greater a part equal to the less . Let AB and c be two unequal given right lines of which AB is the greater : it is required to cut off from the ...
... PROPOSITION III . PROBLEM . Two unequal right lines being given , to cut off from the greater a part equal to the less . Let AB and c be two unequal given right lines of which AB is the greater : it is required to cut off from the ...
Seite 10
... proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this proposition , says , he has thought proper to change its ...
... proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this proposition , says , he has thought proper to change its ...
Seite 11
... PROPOSITION VIII . THEOREM . If two triangles have two sides equal to two sides , each to each , and have their bases equal ; the angle also , which is contained by the equal sides of the one triangle , shall be equal to the angle ...
... PROPOSITION VIII . THEOREM . If two triangles have two sides equal to two sides , each to each , and have their bases equal ; the angle also , which is contained by the equal sides of the one triangle , shall be equal to the angle ...
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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.