## The first six books of the Elements of Euclid, with numerous exercises |

### From inside the book

Results 6-10 of 22

Page 40

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**rectangle**ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ...**contained**by ab , bc , for bk is equal to bc , four times the**rectangle**a b , bc is quadruple of ak : but the ... Page 42

... rectangle con- tained by the whole and one of the parts shall be equal to the square of the other part . LET ab be the given straight line ; it is required to divide it into two parts , so that the

... rectangle con- tained by the whole and one of the parts shall be equal to the square of the other part . LET ab be the given straight line ; it is required to divide it into two parts , so that the

**rectangle contained**by the whole and ... Page 43

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**rectangle contained**by cf fa , for af is equal to fg ; and ad is the of square ab ; therefore fk is equal to ad : take away the common part ak , and the remainder fh is equal to the remainder hd : and hd is the**rectangle contained**by ab ... Page 44

... containing that angle , by twice the

... containing that angle , by twice the

**rectangle contained**by either of these sides , and the straight line inter- cepted between the perpendicular let fall upon it from the opposite angle and the acute angle . LET abc be any triangle ... Page 45

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**rectangle**be , ef , together with the square of eg , is equal ( ii . 5 ) to the square of gf : but gf is equal to gh ...**contained**by be , ef is the parallelogram bd , because ef is equal to ed ; therefore bd is equal to the square ...### Other editions - View all

### 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.