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

Macmillan and Company, limited, 1900 - 304 σεκΏδερ
1  ώιτιξό
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### Ργλοωικό αποσπήσλατα

”εκΏδα 42 - Any two sides of a triangle are together greater than the third side.
”εκΏδα 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.
”εκΏδα 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...
”εκΏδα 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
”εκΏδα 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.
”εκΏδα 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.
”εκΏδα 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.
”εκΏδα 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.
”εκΏδα 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.
”εκΏδα 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.