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 σελίδες |
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Σελίδα 51
... inscribed in a right - lined figure , when every one of the angles of the inscribed figure touch every one of the fides of the figure wherein it is inscribed . So the triangle DEF is infcribed in the triangle ABC . Plate II . Fig . 48 ...
... inscribed in a right - lined figure , when every one of the angles of the inscribed figure touch every one of the fides of the figure wherein it is inscribed . So the triangle DEF is infcribed in the triangle ABC . Plate II . Fig . 48 ...
Σελίδα 52
... inscribed in the circle is equiangular to DEF . Which was to be done . 1 PROP . III . Fig . 52 , 53 . About a circle given IABC to describe a triangle LNM , equiangular to a triangle given DEF . Produce the fide EF on both fides ; at ...
... inscribed in the circle is equiangular to DEF . Which was to be done . 1 PROP . III . Fig . 52 , 53 . About a circle given IABC to describe a triangle LNM , equiangular to a triangle given DEF . Produce the fide EF on both fides ; at ...
Σελίδα 53
... inscribed , shall be found , Thus ; Let AB be 12 , AC 18 , BC 16 , then is AB + BC = 28 . Out of which fubduct 18 = AC = AE + FC , there re- mains 10 = BE + BF . Therefore BE , or BF = 5 ; and consequently FC , or CG = 11. Wherefore GA ...
... inscribed , shall be found , Thus ; Let AB be 12 , AC 18 , BC 16 , then is AB + BC = 28 . Out of which fubduct 18 = AC = AE + FC , there re- mains 10 = BE + BF . Therefore BE , or BF = 5 ; and consequently FC , or CG = 11. Wherefore GA ...
Σελίδα 54
... inscribed in a circle given . Which was to be done . PROP . VII . Fig . 58 . About a circle given EABCD , to describe a square FHIG . Draw the Diameters AC , BD , cutting one the other at right - angles ; through the extremes of these ...
... inscribed in a circle given . Which was to be done . PROP . VII . Fig . 58 . About a circle given EABCD , to describe a square FHIG . Draw the Diameters AC , BD , cutting one the other at right - angles ; through the extremes of these ...
Σελίδα 56
... inscribed in circles by the help of Isosceles triangles , whose angles at the base are multiples of those at the top ... Inscribe a pentagon ABCDE in the circle given ; and from the center draw the right - lines FA , FB , FC , FD ...
... inscribed in circles by the help of Isosceles triangles , whose angles at the base are multiples of those at the top ... Inscribe a pentagon ABCDE in the circle given ; and from the center draw the right - lines FA , FB , FC , FD ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is given ABCD alfo alſo given altitude angle angle BAC arch baſe becauſe biſect circle commenfurable compounded Conftr conſequently Coroll cube demonstrated deſcribed diameter Dodecaedron drawn equal equilateral faid fame fide figure fince firſt folid Foraſmuch fore given angle given in kind given in magnitude given in poſition given Magnitude given ratio greater hath inſcribed leſs likewife Logarithm mean proportional meaſure medial multiplied parallel parallelogram pentagon perpendicular plane Plate prime priſms PROP pyramid rational-line rectangle refidual right-angles right-line AB right-line BC ſaid ſame ſay Schol Scholium ſecond ſeeing ſegment ſhall ſide ſolid ſpace ſphere ſquare ſquare number ſuperficies ſuppoſed theſe thoſe triangle ABC whence Wherefore whole whoſe
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 95 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.