A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'. |
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Page 13
... fore the triangle bad contains 60 ° × 2 = 120 ° . Wherefore , at the given point a in the given right line ab the angle bad is made , which contains 120 ° . Which was to be done . Definition . A chord of a circle is the right line which ...
... fore the triangle bad contains 60 ° × 2 = 120 ° . Wherefore , at the given point a in the given right line ab the angle bad is made , which contains 120 ° . Which was to be done . Definition . A chord of a circle is the right line which ...
Page 33
... fore it is equal to half the line ae ( which is equal to ed ) ; that is , it is equal to fe , which is equal ( by the construction ) to af ; wherefore the given line ab is divided into the three equal parts af , fe , and eb ; that is ...
... fore it is equal to half the line ae ( which is equal to ed ) ; that is , it is equal to fe , which is equal ( by the construction ) to af ; wherefore the given line ab is divided into the three equal parts af , fe , and eb ; that is ...
Page 39
... sums of the sides of the inscribed poly- gons are the circumferences of the circles ; where- fore the circumferences of circles are as the dia- meters TO EUCLID'S ELEMENTS . 39 each the same number of sides, and these numbers ...
... sums of the sides of the inscribed poly- gons are the circumferences of the circles ; where- fore the circumferences of circles are as the dia- meters TO EUCLID'S ELEMENTS . 39 each the same number of sides, and these numbers ...
Page 40
Joseph Denison. fore the circumferences of circles are as the dia- meters of the circles . - Q . E. D. PROPOSITION XXI . - THEOREM . Arcs of circles which subtend equal angles at the centre are as the radii of the circles . Let abd , efg ...
Joseph Denison. fore the circumferences of circles are as the dia- meters of the circles . - Q . E. D. PROPOSITION XXI . - THEOREM . Arcs of circles which subtend equal angles at the centre are as the radii of the circles . Let abd , efg ...
Page 42
... fore the angles dci , icb are each one - third of the angle acb , and the given angle acb is trisected by the lines or radii cd , di , which was to be done . PROPOSITION XXIII . - PRO BLM . To divide the 42 A NEW SUPPLEMENT.
... fore the angles dci , icb are each one - third of the angle acb , and the given angle acb is trisected by the lines or radii cd , di , which was to be done . PROPOSITION XXIII . - PRO BLM . To divide the 42 A NEW SUPPLEMENT.
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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
ae is equal angle abc angle acb angle bad angles cab arc adc bisected centre circle abcd circle age circle klmn clid contains 30 Corollary demonstrated describe a square describe the circle describe the square diagonal diameter ac double the square duplicate ratio equal angles equal sides equal to 60 equal to half equi equilateral triangle given circle abd given circle efgh given line given right line given square abcd half the given hexagon homologous sides hypothenuse isosceles triangle join Let abcd multiple octuple Proposition 14 quadruple the square radii radius ac rectangles ac remaining angle right-angle acb Scholium sextuple side ab side ac similar polygon inscribed similar triangles spaces described square abfg square bdih square described square efgh square gikl square of ac subtend Supplement triangle abc trigon abc trigon inscribed triple the square trisected vertical angle wherefore the angle wherefore the square
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.