The History and Significance of Certain Standard Problems in Algebra, Issue 251 |
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Alcuin algebra Algorism amount amphora annuity arithmetic Arithmetica barter bezants Borghi braccia Brahmagupta Buteo Calandri Cardan Cataneo century CHIG cistern Clavius Columbia Algorism computation Contz demaunde denarii dieb ducati ERSITY UNIV Fibonacci 1202 florins frippier GAN GAN GAN MIC GAN MICHI GAN UNIV Gemma Frisius genuine problems geometric progressions Ghaligai gives Greek Anthology group of problems Hereafter referred Humphrey Baker illustrate interest Köbel lems Liber Abaci libras lire Mahāvīra mathematics MIC UNIV MICHI GAN MICHI UNIV Mikami NIVERS ogni Pacioli Pförtner Pike pound Practica arithmetice 1539 primo prob pseudo-real puzzle Queritur question quot Rabbi ben Ezra recreations Rhind Mathematical Papyrus Riese Robert Recorde RSITY Rudolff Rule of False Rule of Three Saunderson sheep solution solving Tartaglia textbooks tion Tonstall Trattato Trenchant Treviso Arithmetic UNIV ERSIT UNIV SITY UNIV UNIV UNIV variant Venetia verbal problems weight writers
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Page 15 - Now, supposing both these to be carelessly left open, and the water to be turned on at 4 o'clock in the morning : a servant, at 6, finding the water running, puts in the tap : in what time, after this accident, will the tub be filled ? Ans.
Page 73 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Page 73 - B traveled on the same road, and at the same rate, from Huntingdon to London. At the 50th mile stone from London, A overtook a drove of Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours.
Page 69 - PROBLEM I AM a brazen lion ; my spouts are my two eyes, my mouth, and the flat of my right foot. My right eye fills a jar in two days, my left eye in three, and my foot in four. My mouth is capable of filling it in six hours ; tell me how long all four together will take to fill it.
Page 100 - Pike, Nicolas. A new and complete system of arithmetic, composed for the use of the citizens of the United States.
Page 74 - ... which was moving at the rate of 9 miles in 4 hours. B. overtook the same drove of geese at the 45th milestone, and met the same stage-waggon exactly 40 minutes before he came to the 31st milestone ; where was B.
Page 98 - Abraham compilavit et secundum librum qui Indorum dictus est composuit.
Page 69 - I am a brazen lion; my spouts are my two eyes, my mouth, and the flat of my right foot. My right eye fills a jar in two days [1 day =12 hours], my left eye in three, and my foot in four. My mouth is capable of filling it in six hours. Tell me how long all four together will take to fill it.
Page 58 - A man went into an orchard which had seven gates and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples that he had and one apple more. To the second, he gave his remaining apples and one apple more.
Page 97 - The most important development in the use of problems is likely to be the realization that they are an integral and vital part of the course, not mere ornaments, and that they make an appreciable contribution to the disciplinary value of algebra. In the future, puzzle problems will be used because human beings enjoy them ; genuine problems will remain because men demand specific and immediate application of the theory they study; 'and pseudo-real problems will supplement the other two in providing...