# Euclid's Elements, Or, Second Lessons in Geometry: In the Order of Simson's and Playfair's Editions ...

Collins, Brother & Company, 1846 - 138 Seiten
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### Inhalt

 Abschnitt 1 1 Abschnitt 2 7 Abschnitt 3 11 Abschnitt 4 16 Abschnitt 5 28 Abschnitt 6 32 Abschnitt 7 34 Abschnitt 8 41
 Abschnitt 13 63 Abschnitt 14 69 Abschnitt 15 75 Abschnitt 16 86 Abschnitt 17 90 Abschnitt 18 96 Abschnitt 19 97 Abschnitt 20 104

 Abschnitt 9 47 Abschnitt 10 52 Abschnitt 11 60 Abschnitt 12 61
 Abschnitt 21 113 Abschnitt 22 Abschnitt 23 1

### Beliebte Passagen

Seite 90 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Seite 117 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Seite 92 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Seite 79 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.
Seite 87 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally...
Seite 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Seite 94 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 12 - 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.
Seite 133 - If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
Seite 13 - AB be the greater, and from it cut (3. 1.) off DB equal to AC the less, and join DC ; therefore, because A in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides DB, BC are equal to the two AC, CB. each to each ; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC is< equal to the triangle (4. 1.) ACB, the less to 'the greater; which is absurd.