A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'.Whittaker & Company, 1840 - 84 páginas |
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Página 16
... hypothenuse ac is equal to the sum of the squares of the base ae , and of the perpen- dicular ec ; but the base and perpendicular are equal ; wherefore their squares are equal ( 8 Ax . Euclid ) ; wherefore the square of the base ae is ...
... hypothenuse ac is equal to the sum of the squares of the base ae , and of the perpen- dicular ec ; but the base and perpendicular are equal ; wherefore their squares are equal ( 8 Ax . Euclid ) ; wherefore the square of the base ae is ...
Página 17
... radius ac . Because the angle at the centre acb is a right- angle , the square of the hypothenuse ( that is , the chord ) ab is the sum of the squares of the two B sides ac and cb , which are equal sides ; TO EUCLID'S ELEMENTS . 17.
... radius ac . Because the angle at the centre acb is a right- angle , the square of the hypothenuse ( that is , the chord ) ab is the sum of the squares of the two B sides ac and cb , which are equal sides ; TO EUCLID'S ELEMENTS . 17.
Página 21
... hypothenuse be is equal to the sum of the squares of the base ic and of the perpen- dicular bi ( 1 Euclid , 47 ) ; but the perpendicular bi has been demonstrated to be equal to half the hypothenuse bc ; wherefore the square befg de ...
... hypothenuse be is equal to the sum of the squares of the base ic and of the perpen- dicular bi ( 1 Euclid , 47 ) ; but the perpendicular bi has been demonstrated to be equal to half the hypothenuse bc ; wherefore the square befg de ...
Página 28
... hypothenuse ef is equal to the sum of the squares described upon the base eb , and the perpendicular bf ; but the base and perpendicular eb , bf are two sides of the square begf , wherefore they are equal ; wherefore the square ...
... hypothenuse ef is equal to the sum of the squares described upon the base eb , and the perpendicular bf ; but the base and perpendicular eb , bf are two sides of the square begf , wherefore they are equal ; wherefore the square ...
Página 29
... . The square klnm shall be the octuple of the given square abcd . For the square aefg , the hypothenuse or diag- onal of the square abcd , is double the square TO EUCLID'S ELEMENTS . 29 PROPOSITION. XIII.-PROBLEM. ...
... . The square klnm shall be the octuple of the given square abcd . For the square aefg , the hypothenuse or diag- onal of the square abcd , is double the square TO EUCLID'S ELEMENTS . 29 PROPOSITION. XIII.-PROBLEM. ...
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A New Supplement to Euclid's Elements of Geometry, by the Author of 'a New ... Joseph Denison Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.
Página 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.
Página 63 - Ratios that are the same to the same ratio, are the same to one another.
Página 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Página 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.
Página 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...
Página 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.
Página 63 - CE equal to the ratio of the square of AB to the square of AD.
Página 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.