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 |
From inside the book
Page 13
... BC upon EF , the point C shall also coincide with the point F , because BC is equal to EF ( Hyp . ) : And BC coinciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC coincides with the base EF , whereas the ...
... BC upon EF , the point C shall also coincide with the point F , because BC is equal to EF ( Hyp . ) : And BC coinciding with EF , BA and AC shall coincide with ED and DF ; for , if the base BC coincides with the base EF , whereas the ...
Page 14
... BC , CD , each to each , and the angle ACD is equal to the angle BCD ( Constr . ) — therefore the base AD A D B is equal to the base DB : Wherefore the straight line AB is bisected in the point D. Q. E. F. PROP . XI . PROB . To draw a ...
... BC , CD , each to each , and the angle ACD is equal to the angle BCD ( Constr . ) — therefore the base AD A D B is equal to the base DB : Wherefore the straight line AB is bisected in the point D. Q. E. F. PROP . XI . PROB . To draw a ...
Page 19
... BC be pro- duced to D : the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remain- ing angles to the remaining ...
... BC be pro- duced to D : the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remain- ing angles to the remaining ...
Page 25
... BC shall be also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than ... base BC is equal to the base EG And because DF is equal to DG , the angle DFG is equal to the angle DGF ( 1. 5 ) ...
... BC shall be also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than ... base BC is equal to the base EG And because DF is equal to DG , the angle DFG is equal to the angle DGF ( 1. 5 ) ...
Page 26
... base BC greater than the base EF : the angle BAC shall be greater than the angle EDF . A B D C E F For , if it be not greater , it must be either equal to it , or less : But the angle BAC is not equal to the angle EDF , because then the ...
... base BC greater than the base EF : the angle BAC shall be greater than the angle EDF . A B D C E F For , if it be not greater , it must be either equal to it , or less : But the angle BAC is not equal to the angle EDF , because then the ...
Other editions - View all
The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 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.
Page 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.