The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Side 12
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another ( 1.5 ) : But the angle ECD is greater than the angle BCD ; therefore also the angle FDC is greater than the angle BCD ...
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another ( 1.5 ) : But the angle ECD is greater than the angle BCD ; therefore also the angle FDC is greater than the angle BCD ...
Side 13
... angles . Let BAC be the given rectilineal angle : it is required to bisect it . Take any point D in AB , and from AC cut off AE equal to AD ; join DE , and upon the side opposite to that on which A lies ... angle DAF is equal BOOK I. 13.
... angles . Let BAC be the given rectilineal angle : it is required to bisect it . Take any point D in AB , and from AC cut off AE equal to AD ; join DE , and upon the side opposite to that on which A lies ... angle DAF is equal BOOK I. 13.
Side 15
... angle DCF is equal to the angle ECF ; and they are adjacent angles : But , when a straight line , standing on another straight line , makes the adjacent angles equal to one another , each of these angles is called a right angle ( Def ...
... angle DCF is equal to the angle ECF ; and they are adjacent angles : But , when a straight line , standing on another straight line , makes the adjacent angles equal to one another , each of these angles is called a right angle ( Def ...
Side 16
... equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each , and the base CF is equal to the base CG ... angle CBE is equal to the two angles CBA 16 EUCLID'S ELEMENTS .
... equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each , and the base CF is equal to the base CG ... angle CBE is equal to the two angles CBA 16 EUCLID'S ELEMENTS .
Side 17
Euclides John William Colenso (bp. of Natal). the angle CBE is equal to the two angles CBA , ABE , to each of these equals add the angle EBD ; therefore the angles CBE , EBD are equal to the ... angle CBE is equal to the two angles CBA...
Euclides John William Colenso (bp. of Natal). the angle CBE is equal to the two angles CBA , ABE , to each of these equals add the angle EBD ; therefore the angles CBE , EBD are equal to the ... angle CBE is equal to the two angles CBA...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Populære avsnitt
Side 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 33 - 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.
Side 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Side 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Side 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Side 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.