The Young Mathematician's Guide: Being a Plain and Easy Introduction to the Mathematicks ... With an Appendix of Practical Gauging |
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Page 2
... Theorem many Times comprehending whole Sciences ; which deduced at length into Propofitions , and demonftrated after the Manner of the Ancients , might well be- come the Subjects of large Treatifes : For whatfoever Theorem folves the ...
... Theorem many Times comprehending whole Sciences ; which deduced at length into Propofitions , and demonftrated after the Manner of the Ancients , might well be- come the Subjects of large Treatifes : For whatfoever Theorem folves the ...
Page 74
... Theorem . Multiply the Sum of the two Extreams into the Num- Sber of all the Terms ; and divide the Product by z The Quotient will be the Sum of all that Series . Per Carol . I. EXAMPLE I. It is required to find the Number of all the ...
... Theorem . Multiply the Sum of the two Extreams into the Num- Sber of all the Terms ; and divide the Product by z The Quotient will be the Sum of all that Series . Per Carol . I. EXAMPLE I. It is required to find the Number of all the ...
Page 75
... Theorem 1. Find the whole Debt thus : 12,5 + 63 75,5 The Sum of the Extreams . II The Number of Terms . 755 755 2 ) 830,5 ( 415,25 = 415 5s . The whole Debt . Then , per Theorem 2. find the common Difference of each Payment . Thus 63-12 ...
... Theorem 1. Find the whole Debt thus : 12,5 + 63 75,5 The Sum of the Extreams . II The Number of Terms . 755 755 2 ) 830,5 ( 415,25 = 415 5s . The whole Debt . Then , per Theorem 2. find the common Difference of each Payment . Thus 63-12 ...
Page 78
... Theorems or Rules , for finding the Sum of any Series in with- out a continued Addition of all the Terms . · · · Let the Series 2 4 8 16. 32.64 . 128. be given , to find it's Sum . the Sum of all the ... Theorem . { 78 Part I. Arithmetick .
... Theorems or Rules , for finding the Sum of any Series in with- out a continued Addition of all the Terms . · · · Let the Series 2 4 8 16. 32.64 . 128. be given , to find it's Sum . the Sum of all the ... Theorem . { 78 Part I. Arithmetick .
Page 79
... Theorem . { z = Theorem 1 . 512-4 4-2 In Words at length thus , From the Product of the fecond and laft Terms fubtract the Square of the first Term , and that Re- mainder being divided by the fecond Term less the firft , will give the ...
... Theorem . { z = Theorem 1 . 512-4 4-2 In Words at length thus , From the Product of the fecond and laft Terms fubtract the Square of the first Term , and that Re- mainder being divided by the fecond Term less the firft , will give the ...
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Common terms and phrases
alfo Amount Angle Anſwer Arch Area Arithmetick Bafe becauſe Cafe call'd Cathetus Circle Circle's Confequently Cube Cubick Inches Cyphers Decimal defcribe Demonftration Denomination Diameter Difference divided Dividend Divifion Divifor eafily eafy Ellipfis equal Equation Example Extreams faid fame fecond feven feveral fhall fhew fingle firft Term firſt fome Fractions Fruftum ftand fubtract fuch Gallons given hath Height Hence Hyperbola infinite Series Intereft interfect juft laft Latus Rectum leffer lefs Lemma Logarithm Meaſure muft multiply muſt Number of Terms Parabola Parallelogram Periphery Perpendicular Places of Figures plain Point Pound Product Progreffion propofed Proportion Quære Quantities Question Radius Reafon Refolvend reft reprefent Right Line Right-angled Right-line Root Rule Sect Segment Series Side Sine Square Suppofe Surd Tangent thefe Theorem theſe thofe thoſe Tranfverfe Triangle Troy Weight ufually Uncia uſeful Vulgar Fractions whofe whole Numbers
Popular passages
Page 473 - 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, &c.
Page 92 - If 8 men can do a piece of work in 12 days, how long will it take...
Page 168 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 395 - RULE. Multiply the sum of the two extremes by half the number of terms, the product will be the sum of all the terms.
Page 469 - Numbers z — i and z -+- 1 be even, and accordingly their Logarithms, and the Difference of the Logarithms will be had, which let be called y.: -Therefore...
Page 146 - ... axioms : 1. If equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities, the quotients will be equal. 5.
Page 476 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 146 - If equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be taken from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same, or equal quantities, the products will be equal.
Page 469 - Term will give the Logarithm to 20 Places of Figures. But, if z be greater than 10000, the...
Page 114 - The particular Rates of all the Ingredients propofed to be mixed, the Mean Rate of the whole Mixture, and any one .of the Quantities to be mixed being given: Thence to find how much of every one of the other Ingredients is requifite to compofe the Mixture.