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 10
... sides are opposite , viz . the angle ACF to the angle ABG and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , the remainder BF is equal to the remainder CG ...
... sides are opposite , viz . the angle ACF to the angle ABG and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , the remainder BF is equal to the remainder CG ...
Side 11
... side of it , there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another , and also those terminated in the other extremity . D If it be possible , let there be two triangles ACB ...
... side of it , there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another , and also those terminated in the other extremity . D If it be possible , let there be two triangles ACB ...
Side 12
... sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides , equal to them , of the ...
... sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides , equal to them , of the ...
Side 13
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG , then upon the same base EF , and upon the same side of it , there would be two triangles having their sides termi- nated in one extremity ...
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG , then upon the same base EF , and upon the same side of it , there would be two triangles having their sides termi- nated in one extremity ...
Side 16
... side of AB , and from the centre C , at the distance CD , describe the circle EGF meeting AB in F , G ; bisect FG in ... sides FH , HC are equal to the two GH , HC , each to each , and the base CF is equal to the base CG - therefore ( 1 ...
... side of AB , and from the centre C , at the distance CD , describe the circle EGF meeting AB in F , G ; bisect FG in ... sides FH , HC are equal to the two GH , HC , each to each , and the base CF is equal to the base CG - therefore ( 1 ...
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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.