Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ... |
From inside the book
Results 1-5 of 26
Page 41
... rectangle contained by the two straight lines is equal to the rectangles con- tained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let BC be divided into any parts in the ...
... rectangle contained by the two straight lines is equal to the rectangles con- tained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let BC be divided into any parts in the ...
Page 42
... rectangle EH is contained by A , EC : Therefore the rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c ...
... rectangle EH is contained by A , EC : Therefore the rectangle contained by A , BC , is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c ...
Page 43
... rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . Let the straight line AB be divided into any two parts in the point C ; the ...
... rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . Let the straight line AB be divided into any two parts in the point C ; the ...
Page 44
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the squares of AC , CB ; wherefore the four ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the squares of AC , CB ; wherefore the four ...
Page 45
... rectangle AD , DB : To each of these add LG , which is equal to the square of CD ; Therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the square of CD ; But the gnomon CMG and LG make up the ...
... rectangle AD , DB : To each of these add LG , which is equal to the square of CD ; Therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the square of CD ; But the gnomon CMG and LG make up the ...
Other editions - View all
Common terms and phrases
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC Constr describe diameter double draw equal angles equal to F equiangular equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Popular passages
Page 12 - If two triangles have two sides of the one equal to two sides of the...
Page 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 143 - 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 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Page 20 - 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 the two straight lines BD.
Page 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Page 44 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Page 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Page 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.