The First Six Books: Together with the Eleventh and Twelfth |
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Page 5
But , by often conûdering and comparing together the Definitions and Demonstrations as they are in the Greek Editions we now have , I found that Theon ...
But , by often conûdering and comparing together the Definitions and Demonstrations as they are in the Greek Editions we now have , I found that Theon ...
Page 82
And this is all that is to be understood , . when , in the Greek text and translations from it , the angle of • the semicircle is said to be greater than ...
And this is all that is to be understood , . when , in the Greek text and translations from it , the angle of • the semicircle is said to be greater than ...
Page 93
And this is all that is meant , when in the « Greek Book III . « Greek'text , and the translations from OF EUCLID . 93.
And this is all that is meant , when in the « Greek Book III . « Greek'text , and the translations from OF EUCLID . 93.
Page 94
Greek'text , and the translations from it , the angle of the greater segment is said to be greater , and the angle of the less “ segment is said to be less ...
Greek'text , and the translations from it , the angle of the greater segment is said to be greater , and the angle of the less “ segment is said to be less ...
Page 273
... which is in the Greek , because the pyramid , in wbae follows , is supposed to be circumscribed about the cone , and so must have the fame vertex .
... which is in the Greek , because the pyramid , in wbae follows , is supposed to be circumscribed about the cone , and so must have the fame vertex .
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Common terms and phrases
added alſo altitude angle ABC angle BAC baſe becauſe Book caſe centre circle circle ABCD circumference common compounded cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſms produced prop proportionals propoſition pyramid reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole
Popular passages
Page 462 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 160 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Page 157 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Page 190 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.