The Young Mathematician's Guide: Being a Plain and Easy Introduction to the Mathematicks ... With an Appendix of Practical GaugingS. Birt, 1747 - 480 σελίδες |
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Σελίδα 72
... Progression , usually called Arithmetical Proportion Continued . WHEN any Rank or Series of Numbers do either increase or decrease by an equal Interval or common Difference , those Numbers are said to be in Arithmetical Progreffion . A ...
... Progression , usually called Arithmetical Proportion Continued . WHEN any Rank or Series of Numbers do either increase or decrease by an equal Interval or common Difference , those Numbers are said to be in Arithmetical Progreffion . A ...
Σελίδα 73
... Progression , the Sum of the two Extreams will be equal to the Sum of the two Means . As in these , 2.4.6.8 . Or 3.6 9. 12 . Viz . 2 + 8 = 4 + 6 . And 3 + 12 = 6 + 9 . & . Corollary . 1 . From these two Lemma's it is easy to conceive ...
... Progression , the Sum of the two Extreams will be equal to the Sum of the two Means . As in these , 2.4.6.8 . Or 3.6 9. 12 . Viz . 2 + 8 = 4 + 6 . And 3 + 12 = 6 + 9 . & . Corollary . 1 . From these two Lemma's it is easy to conceive ...
Σελίδα 74
... Progression , the two Extreams , and the Number of Terms being given , thence to find the Sum of all the Series . Theorem . { Multiply the Sum of the two Extreams into the Num- ber of all the Terms ; and divide the Product by 2 . The ...
... Progression , the two Extreams , and the Number of Terms being given , thence to find the Sum of all the Series . Theorem . { Multiply the Sum of the two Extreams into the Num- ber of all the Terms ; and divide the Product by 2 . The ...
Σελίδα 75
... Progression . The first Payment to be Twelve Pounds Ten Shillings , and the last to be Sixty - three Pounds . What is the whole Debt , and what must each Payment be ? Per Theorem 1. Find the whole Debt thus : 12,5 + 63 75,5 The Sum of ...
... Progression . The first Payment to be Twelve Pounds Ten Shillings , and the last to be Sixty - three Pounds . What is the whole Debt , and what must each Payment be ? Per Theorem 1. Find the whole Debt thus : 12,5 + 63 75,5 The Sum of ...
Σελίδα 76
... Progression ; but because they would require a great many Words to shew the Reason of them : I therefore refer the Reader to the Second Part , viz . That of Algebra , where he may find their Analytical Investigation . Sect . 2 ...
... Progression ; but because they would require a great many Words to shew the Reason of them : I therefore refer the Reader to the Second Part , viz . That of Algebra , where he may find their Analytical Investigation . Sect . 2 ...
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alſo Amount Angles Anſwer Arch Area Arithmetick Axiom Bafe Baſe becauſe Buſhels Cafe call'd Cathetus CHAP Circle Circle's Conſequently Cube Root Cubick Inches Cyphers Decimal Denominator Diameter Difference divided Dividend Diviſor Ducats eaſy Ellipsis equal Equation Example extract Extreams faid fame firſt Fractions Fruftum fuch Gallons given Reſolvend hath Hence Hyperbola increaſed Inſtance Intereſt juſt laſt Latus Rectum leſs Logarithm Mean Rate Meaſure multiplied muſt Number of Terms obſerved Operation Parabola Periphery Places of Figures plain Point Pound Power Product Progreſſion Proportion propoſed Quantities Queſtion Quotient Figure Radius raiſed repreſent requir'd reſpective reſt Right Line Right-angled Right-line Rule ſaid ſame ſay ſecond Sect Segment Series ſet ſeveral ſhall ſhew Side Sine ſingle ſmall ſome Square Root ſtand Subtraction ſuch Suppoſe Surd Tangent Theorem theſe third thoſe Tranſverſe Triangle Troy Weight Unciæ Uſe Vulgar Fractions Weight whole Numbers whoſe
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 92 - If 8 men can do a piece of work in 12 days, how long will it take...
Σελίδα 168 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 476 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Σελίδα 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.
Σελίδα 469 - Term will give the Logarithm to 20 Places of Figures. But, if z be greater than 10000, the...
Σελίδα 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.