A New Introduction to the Mathematicks: Being Essays on Vulgar and Decimal Arithmetick. Containing, Not Only the Practical Rules, But Also the Reasons and Demonstrations of Them; with So Much of the Theory, and of Universal Arithmetick Or Algebra, as are Necessary for the Better Understanding the Practice and Demonstrations. With a General Preface, Including a Panegyric, on the Usefulness of Mathematical LearningW. Johnston, 1758 - 372 Seiten |
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Seite vii
... less " conceived Prejudices ) fhould be fo far from blunting thy Edge , that they fhould rather be the Whetstone of Virtue , and fharpen thy Endeavours : Why may not the fame Things , which ( for " the Excellency of them ) are the ...
... less " conceived Prejudices ) fhould be fo far from blunting thy Edge , that they fhould rather be the Whetstone of Virtue , and fharpen thy Endeavours : Why may not the fame Things , which ( for " the Excellency of them ) are the ...
Seite xl
... less than r . lefs ; p . 153 , the marginal Refer- ences fhould be 306 and † 305 ; p . 156 1.7 , for 19 r . 9 ; p . 157 1.86 . for 293 r . 312 ; p . 1581. 12 , for of a Bill r . off a Bill ; p . 159 , 1. 11 , for 299 r . 318 ; ibid . in ...
... less than r . lefs ; p . 153 , the marginal Refer- ences fhould be 306 and † 305 ; p . 156 1.7 , for 19 r . 9 ; p . 157 1.86 . for 293 r . 312 ; p . 1581. 12 , for of a Bill r . off a Bill ; p . 159 , 1. 11 , for 299 r . 318 ; ibid . in ...
Seite 7
... less than being , and for greater than ; thus 23 is to be read , 2 is less than 3 ; and 3 2 is , 3 is greater than 2 . The Sign of the Difference of two Quan- tities is , which is made Ufe of when we do not know which is the greatest of ...
... less than being , and for greater than ; thus 23 is to be read , 2 is less than 3 ; and 3 2 is , 3 is greater than 2 . The Sign of the Difference of two Quan- tities is , which is made Ufe of when we do not know which is the greatest of ...
Seite 8
... less than nothing ; denying him to be worth by fo much as the Debts are , what his Goods , Cash , and Debts owing to him would make him to be . 15..In Algebra is the affirmative Sign , and there- fore all Quantities which have this Sign ...
... less than nothing ; denying him to be worth by fo much as the Debts are , what his Goods , Cash , and Debts owing to him would make him to be . 15..In Algebra is the affirmative Sign , and there- fore all Quantities which have this Sign ...
Seite 14
... less than zo , is given by Infpection only ; thus , find the Minorand - Digit in the Left - hand vertical Column , and look against it in the Table for the Subducend ; then , directly over it , on the Top of the Table , will be the re ...
... less than zo , is given by Infpection only ; thus , find the Minorand - Digit in the Left - hand vertical Column , and look against it in the Table for the Subducend ; then , directly over it , on the Top of the Table , will be the re ...
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Häufige Begriffe und Wortgruppen
3grs alfo alſo Amfterdam Anſwer applicate Numbers Arithmetic becauſe betwixt Bufhel Cafe caft Cent CHAP confequently contained Crown Cube Root Days Decimal Demonftration Denominator divided Dividend Divifion Divifor eafily equal Example expreffed faid fame Farthings fecond fhall fhew fhewn fhould fimple fince firft Figure firſt Flemish folved fome Fraction ftand fubtract fuch fufficient fuppofe Gain or Lofs Gallons given Number greater greateſt Square Hence increaſe Integer Intereft laft laſt leaft Number leffer lefs Meaſure merator Method metic Moidore Money muft Multiplicand multiply muſt Number fought Number of Places Number of Points obferve Pence Perfon Pounds Power Price Product Progreffion Quantity Queſtion Quotient Ratio Reaſon Refolvend refpectively remaining right Hand Rule of Three Scholium ſhall Shillings Solution ſtand Sterling Subfidy Suppofition taken Terms thefe theſe Things thofe uſeful Vulgar Fraction whence whofe Root whole Numbers Yards
Beliebte Passagen
Seite xi - ... might be able to transfer it .to other parts of knowledge, as they shall have occasion. For, in all sorts of reasoning, every single argument should be managed as a mathematical demonstration : the connexion and dependence of ideas should be followed, till the mind is brought to the source on which it bottoms, and observes the coherence all along, though in proofs of probability one such train is not enough to settle the judgment, as in demonstrative knowledge.
Seite 300 - OPERATIONS WITH FRACTIONS A) To change a mixed number to an improper fraction, simply multiply the whole number by the denominator of the fraction and add the numerator.
Seite xi - ... we may truly say nature gives us but the seeds of it; we are born to be, if we please, rational creatures, but it is use and exercise only that makes us so, and we are indeed so no farther than industry and application has carried us.
Seite 272 - When first the marriage knot was tied Betwixt my wife and me, My age did hers as far exceed As three times three does three ; , But when ten years and half ten years We man and wife had been, Her age came up as near to mine As eight is to sixteen. Now tell me, I pray, What were our ages on the wedding-day...
Seite xi - I said above, that the faculties of our souls are improved and made useful to us, just after the same manner as our bodies are. Would you have a man write or paint, dance or fence well, or perform any other manual operation dexterously and with ease? let him have ever so much vigour and activity, suppleness and address naturally, yet nobody expects this from him, unless he has been used to it, and has employed time and pains in fashioning and forming his hand, or outward parts, to these motions.
Seite 270 - If the errors are alike, divide the difference of the products by the difference of the errors, and the quotient will be the answer. If the errors are unlike, divide the sum of the products by the sum of the errors, and the quotient will be the answer.
Seite 75 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Seite xi - ... this from him, unlefs he has been ufed to it, and has employed time and pains in fafhioning and forming his hand, or outward parts, to thefe motions. Juft fo it is in the mind ; would you have a man reafon well, you muft ufe him to it betimes, exercife his mind in obferving the connexion of ideas, and following them in train.
Seite xviii - Phaenomena as these did come under the known Laws of Motion, it might very well be taken for granted, that the more obvious Appearances in the same Fabrick are owing to such Causes as are within the Reach of Geometrical Reasoning.
Seite xxiii - ... nor was there ever any thing that has contributed to enlarge my apprehensions of the immense power of God, the magnificence of his creation, and his own transcendent grandeur, so much as the little portion of astronomy which I have been able to attain. And I would not only recommend it to young students, for the same purposes,, but I would persuade all mankind, if it were possible, to gain some degree of acquaintance with the vastness, the distances, and the motions of the planetary worlds, on...