# A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1

Macmillan, 1904 - 456 σελίδες
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### Περιεχόμενα

 BOOK I 5 DEFINITIONS POSTULATES AXIOMS 11 DEFINITIONS 35 PROPOSITIONS 116 44 SECTION II 56 THE AREAS OF PARALLELOGRAMS AND TRIANGLES 72 Theorems and Examples on Book I 95 II 101
 Theorems and Examples on Book III 233 BOOK IV 268 Theorems and Examples on Book IV 297 Elementary Principles of Proportion 317 PROPOSITIONS 353 Theorems and Examples on Book VI 384 IV 396 VI 403

 VI 110 ON AREAS 117 BOOK III 163
 BOOK XI 409 EXERCISES ON BOOK XI 444

### Δημοφιλή αποσπάσματα

Σελίδα 355 - 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.
Σελίδα 342 - 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.
Σελίδα 67 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 164 - 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.
Σελίδα 327 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Σελίδα 164 - 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...
Σελίδα 293 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 81 - 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.
Σελίδα 20 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 244 - 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.