The figures of Euclid with the enunciations, as printed in Euclid's Elements of plane geometry [book 1-4, 6] by W.D. Cooley1840 |
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Page 32
Euclides William Desborough Cooley. PROP . III . THEOR . If a straight line drawn through the centre of a circle ... touch 32 EUCLID'S ELEMENTS .
Euclides William Desborough Cooley. PROP . III . THEOR . If a straight line drawn through the centre of a circle ... touch 32 EUCLID'S ELEMENTS .
Page 35
... straight lines can be drawn to the cir- cumference , must be the centre of the circle . E B F PROP . X. THEOR . The ... touch each other internally , the straight line joining their centres will , when produced , pass through a ...
... straight lines can be drawn to the cir- cumference , must be the centre of the circle . E B F PROP . X. THEOR . The ... touch each other internally , the straight line joining their centres will , when produced , pass through a ...
Page 36
... line joining their centres will pass through a point of contact . B D C G PROP . XIII . THEOR . Two circles cannot touch each other either inter- nally or externally in more than one point . E E B A PROP . XIV . THEOR . Equal straight lines ...
... line joining their centres will pass through a point of contact . B D C G PROP . XIII . THEOR . Two circles cannot touch each other either inter- nally or externally in more than one point . E E B A PROP . XIV . THEOR . Equal straight lines ...
Page 38
... outside of its circum- ference . E B PROP . XVIII . THEOR . If a straight line touches a circle , the ray drawn to the point of contact is perpendicular to the tangent . B E PROP . XIX . THEOR . If a straight line 38 EUCLID'S ELEMENTS .
... outside of its circum- ference . E B PROP . XVIII . THEOR . If a straight line touches a circle , the ray drawn to the point of contact is perpendicular to the tangent . B E PROP . XIX . THEOR . If a straight line 38 EUCLID'S ELEMENTS .
Page 39
Euclides William Desborough Cooley. PROP . XIX . THEOR . If a straight line touches a circle , the straight line drawn from the point of contact perpen- dicular to the tangent , passes through the centre of the circle . PROP . XX ...
Euclides William Desborough Cooley. PROP . XIX . THEOR . If a straight line touches a circle , the straight line drawn from the point of contact perpen- dicular to the tangent , passes through the centre of the circle . PROP . XX ...
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The Figures of Euclid with the Enunciations, as Printed in Euclid's Elements ... Euclides No preview available - 2016 |
Common terms and phrases
angle contained angle subtended bisect a given centre or circumference CHANCERY LANE COR.-Hence cutting line describe a circle divide a given E PROP equal angles reciprocally equal arches equal circles equal sides equal straight lines equal to four equi equilateral and equiangular EUCLID'S ELEMENTS external segment F B PROP F PROP finite straight line four straight lines given circle given finite straight given point given rectilinear angle given rectilinear figure given straight line given triangle half the line homologous sides inscribe an equilateral internal angles isosceles triangle line be bisected line be divided lines be drawn lines be proportional obtuse angle opposite angle parallelogram equal perpendicular point of contact points of section polygons PROB rectangle contained right angles side opposite side subtending Similar triangles spectively equal square of half straight line drawn straight line touches tangent THEOR three given straight touches a circle twice the rectangle whole line XXXIII
Popular passages
Page 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 29 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Page 57 - 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 55 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the...
Page 58 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 26 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Page 54 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Page 56 - The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios Let ABC, DCE, be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle ACB to the angle DEC, and consequently (4.
Page 40 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Page 69 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...