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
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Page 15
... line , which may be produced to any length both ways , and let C be a point without it : it is required to draw from the point C a straight line perpendicular to AB . E Take any point D upon the other side of БООК 1 . 15.
... line , which may be produced to any length both ways , and let C be a point without it : it is required to draw from the point C a straight line perpendicular to AB . E Take any point D upon the other side of БООК 1 . 15.
Page 19
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be pro- duced to D : the exterior angle ACD is greater than either of the interior opposite angles CBA ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be pro- duced to D : the exterior angle ACD is greater than either of the interior opposite angles CBA ...
Page 20
... Produce BC to D : Then , because ACD is the ex- terior angle of the triangle ABC , ACD is greater than the interior and opposite angle ABC ( 1. 16 ) : To each of these add the angle ACB ; therefore the angles ACD , B ACB , are together ...
... Produce BC to D : Then , because ACD is the ex- terior angle of the triangle ABC , ACD is greater than the interior and opposite angle ABC ( 1. 16 ) : To each of these add the angle ACB ; therefore the angles ACD , B ACB , are together ...
Page 21
... , greater than AB . Produce BA to the point D , making AD equal to AC ( 1. 3 ) , and join DC . Then because AD is equal to AC , the angle ADC is equal to the angle ACD : B D But the angle BCD is greater than the angle ACD BOOK I. 21.
... , greater than AB . Produce BA to the point D , making AD equal to AC ( 1. 3 ) , and join DC . Then because AD is equal to AC , the angle ADC is equal to the angle ACD : B D But the angle BCD is greater than the angle ACD BOOK I. 21.
Page 22
... Produce BD to E : Then , because any two sides of a triangle are together greater than the third side ( 1. 20 ) , the two sides , BA , AE , of the triangle ABE are greater than BE : To each of these add EC ; therefore the sides BA , AC ...
... Produce BD to E : Then , because any two sides of a triangle are together greater than the third side ( 1. 20 ) , the two sides , BA , AE , of the triangle ABE are greater than BE : To each of these add EC ; therefore the sides BA , AC ...
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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.