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

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A New Supplement to Euclid's Elements of Geometry, by the Author of 'a New ... Joseph Denison No preview available - 2015 |

### Common terms and phrases

angle abc angle acb angle bad base bisected centre circle abcd circumference clid construction contains 30 cord Corollary demonstrated describe a square describe the circle describe the square diagonal diameter diameter ac divided double the square duplicate ratio equal angles equal to half equilateral triangle Euclid fore four given circle given circle abd given circle efgh given line given square abcd hexagon homologous sides hypothenuse iklm join Let abcd manner multiple nine one-third PROBLEM produce Proposition radii radius ac remaining angle represent right line right-angle scribed sextuple side ab side bc similar triangles square described square efgh square gikl square of ac subtend Supplement tion triangle abc trigon abc triple the square trisected wherefore the angle wherefore the square whole

### Popular passages

Page 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.

Page 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.

Page 63 - Ratios that are the same to the same ratio, are the same to one another.

Page 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.

Page 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.

Page 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...

Page 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.

Page 63 - CE equal to the ratio of the square of AB to the square of AD.

Page 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.