## A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Book 1 |

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### Common terms and phrases

ABCD adjacent alternate base bisected bisectors Book called centre chord circumference circumscribed coincide common Constr Construction Describe a circle diagonal diameter difference distance divided double draw equal equilateral Euclid's EXERCISES exterior angle external extremities fall figure find the locus fixed formed four given circle given point given straight line greater half Hence impossible inches inscribed intersect isosceles triangle Join length less Let ABC meet middle point NOTE opposite sides parallel parallelogram pass perp point of contact PROBLEM produced Proof Prop PROPOSITION prove quadrilateral radius rect rectangle contained regular remaining respectively right angles segment shew shewn Similarly square straight line drawn tangent THEOREM third touch triangle ABC twice vertex vertical angle whole

### Popular passages

Page 42 - Any two sides of a triangle are together greater than the third side.

Page 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.

Page 162 - 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 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.

Page 65 - 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.

Page 68 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.

Page 143 - 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 8 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Page 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.