Elements of Geometry, Containing the First Six Books of EuclidBaldwin, Cradock, and Joy, 1826 - 180 pages |
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Page xv
... four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The latter also wrote a work of a similar kind , consisting of six books , on the His- tory of Geometry , and another of the same number of books on that of ...
... four of which treated on Geometry , six on Astronomy , and one on Arithmetic . The latter also wrote a work of a similar kind , consisting of six books , on the His- tory of Geometry , and another of the same number of books on that of ...
Page xvi
... four eminent geometricians , viz . Dinostratus , Nicomedes , Pappus , and Diocles , deserve particular praise for their merit ; but the reader must excuse my not entering into an expla- nation , or exhibiting to him a view of their ...
... four eminent geometricians , viz . Dinostratus , Nicomedes , Pappus , and Diocles , deserve particular praise for their merit ; but the reader must excuse my not entering into an expla- nation , or exhibiting to him a view of their ...
Page xx
... four of which have been transmitted to us in the language in which they were written ; and the following three had been preserved only in an Arabic translation made about the year 1250 , and translated into Latin about the middle of the ...
... four of which have been transmitted to us in the language in which they were written ; and the following three had been preserved only in an Arabic translation made about the year 1250 , and translated into Latin about the middle of the ...
Page xxi
... four hundred years without meeting with one person who contributed anything to the advancement of the sciences . Theon , how- ever , appeared about 380 years after Christ ; and by his skill and perseverance in mathematics and philosophy ...
... four hundred years without meeting with one person who contributed anything to the advancement of the sciences . Theon , how- ever , appeared about 380 years after Christ ; and by his skill and perseverance in mathematics and philosophy ...
Page 2
... four right lines . 22. Multilateral figures , or polygons , by more than four right lines . 23. Of trilateral figures , an equilateral triangle is that which has three equal sides . 24. An isosceles triangle is that which has only two ...
... four right lines . 22. Multilateral figures , or polygons , by more than four right lines . 23. Of trilateral figures , an equilateral triangle is that which has three equal sides . 24. An isosceles triangle is that which has only two ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.