The New Mathematician's Guide: Containing the Elements of Universal Mathematics, and Demonstrating Sir Isaac Newton's Method of Finding Divisors. With Rules for Extracting the Root of a Binomial, and for Determining the Form of an Assumed Infinite Series |
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The New Mathematician's Guide: Containing the Elements of Universal ... Willem Jacob 's Gravesande No preview available - 2023 |
The New Mathematician's Guide: Containing the Elements of Universal ... Willem Jacob 's Gravesande No preview available - 2015 |
The New Mathematician's Guide: Containing the Elements of Universal ... Willem Jacob 's Gravesande No preview available - 2018 |
Common terms and phrases
affirmative affum'd alfo Algebra alſo Arithmetic Progreffion becauſe betwixt Binomial Cafe chang'd common Divifor compound Quantities confequently Conftruction correfponding Cube cubic Foot Demonftration Denominator determin'd difcover difcover'd Difference Dimenfions divided Dividend Divifion Equa equal EXAMPLE exceeds explain'd expreffed extracted faid fame manner fame Quantity fecond feek feparated fhall fifth Column fimilar fimple fingle firft Term firſt folv'd fome fometimes form'd fquare Root Fractions fubftitute fubftracted fuch fuppofe Geometric given greateſt higheft inftead laft Term leaft leffer lefs Letter Line Meaſure Member Method muft multiplied muſt neceffarily negative Number fought obferv'd oppofite Parallelogram perpendicular pleaſure poffible pofitive Power Problem produc'd Product Proportion Quan Quantity propos'd Quotient radical Sign rational reafon reduced Rule Sign of Equality Solution Square thefe Equations theſe third thofe thoſe tions tity Triangle unknown Quantity Values vifors whence wherefore
Popular passages
Page 36 - If four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus...
Page 97 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference...
Page 71 - The Value of the unknown Quantity is called the Root of the Equation, and it is evident that an Equation of two Dimenfions has two Roots. 2 14. And as a Negative Quantity may be de» fign'd by a Letter, the Root is fometimes nega-r tive ; there are therefore four different Cafes.
Page 97 - Propojition a Line may be divided into any Number of equal Parts, by taking the fame Number of equal Parts at pleafure on another Line.
Page 97 - BC with the same radius. Then a line through A touching this arc will be the required parallel. Or, use a straight edge and triangle.
Page 37 - Exponent is greater ; and vice verfa. 132. Ratio's are faid to be equal, if their Exponents are equal ; for in that cafe both Confequents are contained in the fame manner in their Antecedents. 133. Four Quantities, of -which the firft has the fame Ratio to the fecond, that the third has to the fourth, are faid to be in Geometrical Proportion ; or fimply to form a Proportion. 134. This Proportion is thus mark'd : : a, b : : c, d fignifies that a has the fame Ratio to b, that c has to d.
Page 142 - Quantity will not admit of a Divifor of two Dimenfions. The fame Method may be extended to the Invention of Divifors of more Dimenfions, by feeking in the aforefaid...
Page 134 - Quantity гюЬЬ are defined, divide it by 3, and the Quotient 7 abb by 7, and the Quotient abb by a, and the Quotient bb by b, and there will remain the prime Quotient b. Therefore the prime Divifors are i, 3, 7...
Page 141 - Difference between 27 and 17, that is, 10, divides 170; but the Difference between 12 and — 13, that is, 25, does not divide 190. Wherefore I reject the latter Progreffion. According to the former, If С is — 7, and If В is nothing ; the Terms of the Progreffion having no Difference.