The Young Mathematician's Guide: Being a Plain and Easie Introduction to the Mathematicks |
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Page 58
... Series of Equal Numbers , as 444 , & c . The first 4 towards the Left is Ten times the Value of the 4 in the middle , and that 4 in the middle is Ten times the Value of the laft 4 to the Right of it , and but the Tenth Part of that 4 on ...
... Series of Equal Numbers , as 444 , & c . The first 4 towards the Left is Ten times the Value of the 4 in the middle , and that 4 in the middle is Ten times the Value of the laft 4 to the Right of it , and but the Tenth Part of that 4 on ...
Page 72
... Series of Numbers do either Increase or Decrease by an Equal Interval or Common Difference ; thofe Numbers are faid to be in Arithmetical Progreffion . As As Here the Interval or 51.2.3.4.5.6.7 . & c . 72 Part I. Arithmetick .
... Series of Numbers do either Increase or Decrease by an Equal Interval or Common Difference ; thofe Numbers are faid to be in Arithmetical Progreffion . As As Here the Interval or 51.2.3.4.5.6.7 . & c . 72 Part I. Arithmetick .
Page 73
... Series , whofe Common Difference is 5. & c . · 4 If · any Lemma 1 . three Numbers be in Arithmetical Progreffion ; the Sum of the two Extreams ( viz . the First and Laft ) will be equal to the Double of the Mean or middle Number . As in ...
... Series , whofe Common Difference is 5. & c . · 4 If · any Lemma 1 . three Numbers be in Arithmetical Progreffion ; the Sum of the two Extreams ( viz . the First and Laft ) will be equal to the Double of the Mean or middle Number . As in ...
Page 74
... Series of Numbers in Arithmetick Progreffion , 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 Number of all the Terms ; and ...
... Series of Numbers in Arithmetick Progreffion , 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 Number of all the Terms ; and ...
Page 76
... Series of Numbers do either Increase by one Common Multiplicator , or Decrease by one common Divifor ; thofe Numbers arc faid to be in Geometrical Proportion continu'd . As $ 2.4.8.16 . 32. & c . here 2 is the common Multiplier 64 4 ...
... Series of Numbers do either Increase by one Common Multiplicator , or Decrease by one common Divifor ; thofe Numbers arc faid to be in Geometrical Proportion continu'd . As $ 2.4.8.16 . 32. & c . here 2 is the common Multiplier 64 4 ...
Common terms and phrases
alfo Amount Anfwer Arch Area Arithmetick Bafe becauſe Cafe call'd Cathetus Chap Circle Circle's Compound Intereft Confequently Cube Cube Root Cyphers Decimal Defcribe Demonftration Denomination Difference Divided Dividend Divifion Divifor Dollers Ducats eafie eafily Ellipfis Equal Equation Euclid Example Extreams faid fame feveral fhall fhew Firft Firſt fome Fractions ftand fuch Gallon Geometrical given hath Hence Hyperbola juft Laft Laft Term Latus Rectum Learner Lefs Meaſure muft Multiplicand Multiply muſt Number of Terms obferve Operation Parabola Parallelogram perform'd Periphery Perpendicular Point Pound Power Product Progreffion propofed Proportion Quantities Queft Quere Question Quotient Figure Radius Rate Reafon Refolvend refpective reft reprefent requir'd Right Angles Right Line Right-line Root Rule Second Sect Segment Series Shillings Sides Square ſtand Subftract Suppofe Surd thefe Theorem theſe Third thofe thoſe Troy Weight Uncia's uſed Vulgar Fractions whofe whole Numbers
Popular passages
Page 166 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 307 - The conviction of a truth may be irresistible, and yet not immediate. Thus, my conviction that the three angles of every plain triangle are equal to two right angles, is irresistible, but it is not immediate ; I am convinced of it by demonstrative reasoning. There are other truths in mathematics of which we have not only an irresistible but an immediate conviction. Such are the axioms. Our belief of the axioms in mathematics is not grounded upon argument — arguments...
Page 98 - If 2 men can do 12 rods of ditching in 6 days ; how many rods may be done by 8 men in 24 days ? Ans.
Page 48 - FRACTIONS, or broken numbers, are expressions for any assignable parts of an unit ; and are represented by two numbers, placed one above the other, with a line drawn between them. The number above the line is called the numerator, and that below the line the denominator.
Page 81 - Year, and fo on from Year to Year until the End of the Time, allowing the Increafc to be but in a ten-fold Proportion. It is required to find the Sum of the whole Produce.
Page 252 - Penfions, &c. are faid to be in Arrears, •** when they are payable or due, either Yearly, or Half-yearly) &c.
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. Note, This is ufually called Alligation Partial.
Page 284 - tis 5 to 4, that one of 26 years old will die before one of 16 ; and 6 to 5 that one of 36 will die before one of 26 ; and 3 to 2, that the same person of 36 shall die before him of 16 : And so forward according to the Roots...
Page 82 - The method of finding out the number of changes, is by a continual multiplication of all the terms in a series of arithmetical...