The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method ... |
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Page vii
... Series for the Circle ( in Pag . 100. ) . for the Hyperbola ( in Pag . 109. ) and the Theo rems for measuring the Circular , Elliptic , and Hyperbolic Spindles ( in Pag . 156. ) Then are given the Investigation of Theorems , for redu ...
... Series for the Circle ( in Pag . 100. ) . for the Hyperbola ( in Pag . 109. ) and the Theo rems for measuring the Circular , Elliptic , and Hyperbolic Spindles ( in Pag . 156. ) Then are given the Investigation of Theorems , for redu ...
Page 29
... Series , whofe firft Term is 1 , and Ratio the Root it felf a , as I , a , aa , aaa , aaaa , aaaaa , & c . thus for Example , aaaa , being the 4th Term from 1 , is expreffed by a * ; alfo aaaaa , being the 5th Term from 1 , is expreffed ...
... Series , whofe firft Term is 1 , and Ratio the Root it felf a , as I , a , aa , aaa , aaaa , aaaaa , & c . thus for Example , aaaa , being the 4th Term from 1 , is expreffed by a * ; alfo aaaaa , being the 5th Term from 1 , is expreffed ...
Page 30
... ( fuppofe 10 , ) an infinite , or only a very great Number of Proportionals 1000000 be ta- ken , thereby forming a Geometrical Series , fome of them must approach very near to the natural Num- bers 1 them 30 The THEORY and Ch . III ,
... ( fuppofe 10 , ) an infinite , or only a very great Number of Proportionals 1000000 be ta- ken , thereby forming a Geometrical Series , fome of them must approach very near to the natural Num- bers 1 them 30 The THEORY and Ch . III ,
Page 31
... Series , yet on the above Suppofition , they will obtain Places , very near , in fuch a Se- ries ; and then , Definition . The Place from 1 , which any of them bas in that Series , which is ever the Index of the fecond Term , is called ...
... Series , yet on the above Suppofition , they will obtain Places , very near , in fuch a Se- ries ; and then , Definition . The Place from 1 , which any of them bas in that Series , which is ever the Index of the fecond Term , is called ...
Page 32
... Series is its Logarithm , and that is ever the Index of a the fecond Term ; whence L .: A + L : B = L : AX B. Q. E. 0 . PRO P. II . The Logarithm of the Quotient of any two Num- bers , is equal to the Logarithm of the Divifor , taken ...
... Series is its Logarithm , and that is ever the Index of a the fecond Term ; whence L .: A + L : B = L : AX B. Q. E. 0 . PRO P. II . The Logarithm of the Quotient of any two Num- bers , is equal to the Logarithm of the Divifor , taken ...
Other editions - View all
The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method ... Robert Shirtcliffe No preview available - 2018 |
The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method Robert Shirtcliffe No preview available - 2018 |
The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method Robert Shirtcliffe No preview available - 2023 |
Common terms and phrases
Abfciffa againſt Ale Gall alfo alſo Angle Area Bafe Baſe becauſe betwixt Breadth Bung-Diameter Cafk called Caſk Chap Circle circular Segment Cone Conic Conic Sections Conoid Content Corol correfponding Curve Decimal denote Diam Diſtance divided Divifion Divifor dry Inches Ellipfe equal Example expreffed faid fame fecond fhall fhew fhewn Figure fimilar fince firft firſt fome Fruftum ftand fuch fufficient fuppofe fure Gauging given gives Height hence Hoof Hyperbola Hyperbolic Segment laft laſt Lemma Length Logarithms mean Diameter Meaſure Method multiplied muſt Number oppofite Ordinate orems parabolic parallel perpendicular Plane Points Product Prop Propofition Quotient Radius Reaſon refpectively Root Rule Scholium Section Segment ſhall Side Sliding-Rule Solid Spheroid Spindle Square taken Terms thefe Theorem thereof theſe thofe thoſe thro tranfverfe Axis Triangle Ullage uſe verfed Sine Vertex wet Inches whence whofe Wine Gallons
Popular passages
Page 59 - 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, fourths, &c.
Page 7 - In multiplication of decimals, we know that the number of decimal places in the product is equal to the sum of those in both the factors.
Page 97 - J of the square of their difference, then multiply by the hight, and divide as in the last rule. Having the diameter of a circle given, to find the area. RULE. — Multiply half the diameter by half the circumference, and the product is the area ; or, which is the same thing, multiply the square of the diameter by .7854, and the product is the area.
Page 282 - Sort is, to multiply the two Weights together, and extract the Square Root of. the Product, which Root will be the true Weight.
Page 283 - Backs time ufed, and become more and more uneven as they grow older, efpecially fuch as are not every where well and equally fupported ; many of them...
Page 187 - Sum of thofe next to them, C the Sum of the two next following the laft, and fo on ; then we (hall have the following fables of Areas, for the feveral Numbers of Ordinates prefixt againft them, viz.
Page 86 - Progreflion from o, is equal to the Product of the laft Term by the Number of Terms, and this divided by the Index (m) plus Unity.
Page 272 - To half the Sum of the Squares of the Top and Bottom Diams.
Page 95 - The latter being taken from the former, leaves 3.14.15.9265.5 for the Length of half the Circumference of a Circle whofe Radius is Unity : Therefore the Diameter of any Circle is to its Circutuftrence as I is to 3.1415.9265.5 nearly.
Page 86 - Numbr infinitely greAt, therefore the firft Term of the above Value of /, muft be infinitely greater than any of the...