## Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1870 |

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Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides No preview available - 2016 |

### Common terms and phrases

ABē ABCD ACē ADē adjacent angles Algebra altitude angles equal angular points Arith Arithmetic Axioms base BC BCē bisect centre circle circumference Class-Book of Modern Concl construct defendant's book demonstration describe diagonal diameter difference distance draw a st drawn equilateral Euclid Euclid's Elements given line given point given rectilineal given st gnomon greater hypotenuse interior angles intersect isosceles triangle John Heywood join less line BC line be divided literary magnitude measure monad opposite angles opposite sides parallelogram perpendicular plaintiffs Plane Geometry premiss PROB produced Prop radius Recap rectangle rectangle contained rectilineal figure regular polygon right angles segment side AC sides equal square straight line surface truth twice Vice-Chancellor Wherefore

### Popular passages

Page 175 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Page 95 - ... equal angles in each ; then shall the other sides be equal, each to each ; and also the third angle of the one to the third angle of the other.

Page 178 - 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 are equal to twice the rectangle AB, BC, together with the square of AC.

Page 95 - 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 159 - 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...

Page 102 - 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 182 - 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 230 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

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