## Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green |

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ABCD adjacent angles Algebra altitude angle equal angular point Arith Arithmetic ascertain Axiom bisect centre circumference Concl Cons construct Demonstration.—P describe diagonal diameter distance drawn equal bases equilateral Euclid Euclid's Elements exterior angle extremity Geometry given line given point given rectilineal given st greater hypotenuse inch intersect isosceles triangle JOHN HEYWOOD Kecap length less line A B line be divided line falling lines AC magnitude major premiss measure monad opposite angles opposite sides parallel parallelogram perpendicular plane Plane Geometry polygon Prob produced Prop radius Recap rectangle rectangle contained rectilineal angle rectilineal figure regular polygon right angles scale of equal Scholium Scholium.—1 segment sides and angles sides equal surface Syllogism trapezium twice vertical angle Wherefore

### Popular passages

Page 93 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...

Page 105 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Page 161 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.

Page 93 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.

Page 100 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...

Page 180 - 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.

Page 18 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 142 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Page 44 - LET it be granted that a straight line may be drawn from any one point to any other point.