Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated: with Archimede's Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Also, Euclide's Data, and A Brief Treatise [added by Flussas] of Regular SolidsW. and J. Mount, 1751 - 384 páginas |
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... measure fatisfied both my own Intentions , and the Defire of the Studious . As for fome certain Problems and Theorems that are added in the Scholions ( or short Expofitions ) either appertaining ( by reason of their frequent Ufe ) to ...
... measure fatisfied both my own Intentions , and the Defire of the Studious . As for fome certain Problems and Theorems that are added in the Scholions ( or short Expofitions ) either appertaining ( by reason of their frequent Ufe ) to ...
Página 95
... measure , which is 5 , measures 10 by 2 , and 15 by 3 . V , A multiple is a greater number compared with a leffer , when the leffer measures the greater . VI . An even number is that which may be divided into two equal parts . VII . But ...
... measure , which is 5 , measures 10 by 2 , and 15 by 3 . V , A multiple is a greater number compared with a leffer , when the leffer measures the greater . VI . An even number is that which may be divided into two equal parts . VII . But ...
Página 96
... measure . XIII . A compofed number is that which fome certain number measureth . XIV . Numbers compofed the one to the other , are thofe , which fome number , being a common measure to them both , doth measure . In this , and the ...
... measure . XIII . A compofed number is that which fome certain number measureth . XIV . Numbers compofed the one to the other , are thofe , which fome number , being a common measure to them both , doth measure . In this , and the ...
Página 97
... measures the fourth , equally : and vice versa . So A : B :: C : D. that is , 39 9 : : 5:15 . XXI . Like plane ... measure another , by a third number , which when it either multiplies , or is multiplied by the measuring number ...
... measures the fourth , equally : and vice versa . So A : B :: C : D. that is , 39 9 : : 5:15 . XXI . Like plane ... measure another , by a third number , which when it either multiplies , or is multiplied by the measuring number ...
Página 98
... measures another , that number by which it measureth shall measure the fame by the units that are in the number measuring , that is , by the num- ber it felf that measures . حرية 9. If a number measuring another , multiply that by which ...
... measures another , that number by which it measureth shall measure the fame by the units that are in the number measuring , that is , by the num- ber it felf that measures . حرية 9. If a number measuring another , multiply that by which ...
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Términos y frases comunes
ABC is given ABCD alfo given alſo altitude angle BAC bafes baſe becauſe circle commenfurable confequently Conftr Coroll cube defcribed demonftrated diameter Dodecaedron drawn equal equilateral faid fame fecond feeing fegment fhall fide figure fince firft firſt folid angle Forafmuch fore fquare fuperficies fuppofe given angle given in kind given in magnitude given in pofition given Magnitude given ratio greater hath Hypothefis Icofaedron infcribed lefs likewife Logarithm mean proportional meaſure medial multiplied oppofite parallel parallelogram pentagon perpendicular plane Plate prifms PROP pyramid rectangle refidual refidual-line right-angles right-line AB right-line BC Schol Scholium ſhall ſpace Space AC ſphere ſquare theſe thofe thoſe triangle ABC whence Wherefore whofe whole whoſe
Pasajes populares
Página 18 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 281 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn...
Página 2 - XV. A Circle is a plain figure contained under one line, which is called a circumference ; unto which all lines, drawn from one point within the figure, and falling upon the circumference thereof, are equal the one to the other. XVI. And that point is called the center of the circle. XVII. A Diameter of a circle is a right-line drawn thro' the center thereof, and ending at the circumference on either fide, dividing the circle into two equal parts.
Página 95 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Página 381 - Rule. Multiply the Logarithm of the given number by the Index of the proposed power, and the product will be the Logarithm, whose natural number is the power required.
Página 197 - ... than the other side, an obtuse-angled ; and if greater, an acute-angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle, which revolves. XXI. A cylinder is a solid figure described by the revolution of a rightangled parallelogram about one of its sides which remains fixed.
Página 196 - ... are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point. XII. A Pyramid is a folid Figure comprehended under divers Planes fet upon one Plane, and put together at one Point. ' «. XIII. A Prifm is a folid Figure contained under Planes, whereof the two oppofite are equal, fimilar, and parallel, and the others Parallelograms.
Página 353 - To divide one number by another.* Subtract the logarithm of the divisor from the logarithm of the dividend, and the remainder will be the logarithm of the quotient.
Página 2 - ... parts. XVIII. A Semicircle is a figure which is contained under the diameter and that part of the circumference which is cut off by the diameter. In the circle EABCD, E is the center, AC the diameter > ABC the femi circle.
Página 51 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.