# A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'.

Whittaker & Company, 1840 - 84 Seiten

### Inhalt

 Abschnitt 1 11 Abschnitt 2 23 Abschnitt 3 29 Abschnitt 4 34 Abschnitt 5 38
 Abschnitt 6 39 Abschnitt 7 43 Abschnitt 8 49 Abschnitt 9 66 Abschnitt 10 70

### Beliebte Passagen

Seite 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.
Seite 41 - PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that DE is of F: C shall be to F, as AB to DE.
Seite 63 - Ratios that are the same to the same ratio, are the same to one another.
Seite 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Seite 13 - PQ the given straight line, and A the given point in it. It Is required to describe a circle to touch ihe 0 DEB, and also to touch PQ at A.
Seite 56 - In any triangle the square on a side opposite to an acute angle is less than the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing...
Seite 57 - PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base.
Seite 63 - CE equal to the ratio of the square of AB to the square of AD.
Seite 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.