The first six books of the Elements of Euclid, with numerous exercises |
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Page 1
... taken , the straight line between them lies wholly in that superficies . VIII . A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal ...
... taken , the straight line between them lies wholly in that superficies . VIII . A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . IX . A plane rectilineal ...
Page 4
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
... taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one ...
Page 49
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET abc be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the ...
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET abc be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the ...
Page 51
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
Page 52
... taken , & c . Q. E. D. PROPOSITION VIII . - THEOREM . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave ...
... taken , & c . Q. E. D. PROPOSITION VIII . - THEOREM . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave ...
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Common terms and phrases
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Popular passages
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 : XVI.
Page 42 - 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.
Page 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 38 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Page 15 - If, from the ends of the 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. Let...
Page 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 126 - 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.