## The Mathematical Questions Proposed in the Ladies' Diary: And Their Original Answers, Together with Some New Solutions, from Its Commencement in the Year 1704 to 1816, Volume 1 |

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abscissa Additional Solution altitude angle Answered arch axis azimuth base breadth bung cask centre chains circle consequently construction cosine cube curve described diagonal diameter difference Diophantus distance divided draw earth Eathorpe ellipse equal equation Eucl feet fluxion frustum gallons given gives gravity greater greatest half height hence hour angle hyperbola hypothenuse inches inscribed John Turner latitude latus rectum length magic square meridian miles multiplied parabola parallel perpendicular Peter Kay plane pole PRIZE QUESTION proportion quantity Questions proposed radius ratio rectangle right-angled triangle root segment ship side similar triangles sine sine and cosine solidity subtracted sun's suppose tang tangent theorem three numbers tion transverse trapezium trigonometry Tripontium velocity whence whole number yards

### Popular passages

Page 118 - Close to the gates a spacious garden lies, From storms defended and inclement skies. Four acres was th...

Page 119 - This through the gardens leads its streams around, Visits each plant, and waters all the ground: While that in pipes beneath the palace flows, And thence its current on the town bestows ; To various use their various streams they bring, The people one, and one supplies the king...

Page 118 - Four acres was th' allotted space of ground, Fenc'd with a green enclosure all around : 145 Tall thriving trees confess'd the fruitful mould ; The red'ning apple ripens here to gold : Here the blue fig with luscious juice o'erflows, 'With deeper red the full pomegranate glows, The branch here bends beneath the weighty pear, And verdant olives flourish round the year.

Page 119 - With all th' united labours of the year, Some to unload the fertile branches run, Some dry the blackening clusters in the sun. Others to tread the liquid harvest join, The groaning presses foam with floods of wine. Here are the vines in early flower descried, Here grapes discoloured on the sunny side, And there in Autumn's richest purple dy'd.

Page 119 - Pear supplies, On Apples Apples, Figs on Figs arise: The same mild Season gives the Blooms to blow, The Buds to harden, and the Fruits to grow. Here order'd Vines in equal Ranks appear With all th...

Page 23 - Ans. 41.9968. 6. fin a level garden there are two lofty firs, having their tops ornamented with gilt balls; one is 100 feet high, the other 80, and they are 120 feet distant at the bottom ; now the owner wants to place a fountain in a right line between the trees, to be equally distant from -the top of each ; what will be its distance from the bottom of each tree, and also from each of the balls ? t From the bottom of the lower tree 75 feet.

Page 118 - Here the blue fig with luscious juice o'erflows, With deeper red the full pomegranate glows, The branch here bends beneath the weighty pear, And verdant olives flourish round the year. The balmy spirit of the western gale Eternal breathes on fruits untaught to fail: Each dropping pear a following pear supplies, On apples apples, figs on figs arise: 292 The same mild season gives the blooms to blow, The buds to harden, and the fruits to grow. Here order'd vines in equal ranks appear, With all th...

Page 12 - Accordingly, the next morning, with a joyful countenance, he brought me the construction neatly drawn out on a large sheet of pasteboard, saying he esteemed it a treasure, having found it quite right, as every point and line agreed to a hair'sbreadth by measurement on the scale.

Page 17 - I asked him to make me a flat-bottomed kettle. Let the top and the bottom diameters be In just such proportion as five is to three : Twelve inches the depth I proposed, and no more, And to hold in ale gallons seven less than a score. He promised to do...

Page 12 - ... much that it might not be correctly true. On referring him to the accompanying demonstration to satisfy himself of its geometrical truth, I was much surprised by his reply, that he could not understand that, but he would make the drawing correctly on a large scale, which was always his way to try if such things were true. In my surprise I asked where he had learned Geometry, and by what Euclid, or other book ; to which he frankly replied he had never learned any Geometry, nor could ever understand...