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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Página 7
... given , from the greater DC , to take away the right - line DE , equal to ... angle D contained under the equal right - lines ; they shall have the bafe ... angle A ( a ) —D . Moreover the point F shall fall upon the point C ...
... given , from the greater DC , to take away the right - line DE , equal to ... angle D contained under the equal right - lines ; they shall have the bafe ... angle A ( a ) —D . Moreover the point F shall fall upon the point C ...
Página 9
... angle FDC— ( 4 ) ACD , that d9 ax . is , the angle FDC — ADC . ( d ) Which is impoffible . 3. Cafe . If D ( Fig ... given BAC . ( a ) Take AD to AE , and draw the line DE ; upon which ( 6 ) make an equilateral triangle DFE , draw the right ...
... angle FDC— ( 4 ) ACD , that d9 ax . is , the angle FDC — ADC . ( d ) Which is impoffible . 3. Cafe . If D ( Fig ... given BAC . ( a ) Take AD to AE , and draw the line DE ; upon which ( 6 ) make an equilateral triangle DFE , draw the right ...
Página 10
... given AB ( a ) erect an equilateral tri- angle ABC ; and ( b ) bifect the angle C with the right- line CD . That line shall also bisect the line given AB . For AC ( c ) BC , and the fide CD is common , and the angle ACD ( c ) BCD ...
... given AB ( a ) erect an equilateral tri- angle ABC ; and ( b ) bifect the angle C with the right- line CD . That line shall also bisect the line given AB . For AC ( c ) BC , and the fide CD is common , and the angle ACD ( c ) BCD ...
Página 14
... angle D be equal to ACD ; ( c ) therefore is the whole angle BCDD ; ( d ) therefore BD ( e ) ( BA + AC ) —BC . Which ... given A , B , C . Of which it is necessary that any two taken together be longer than the third . From the infinite line ...
... angle D be equal to ACD ; ( c ) therefore is the whole angle BCDD ; ( d ) therefore BD ( e ) ( BA + AC ) —BC . Which ... given A , B , C . Of which it is necessary that any two taken together be longer than the third . From the infinite line ...
Página 17
... angle AGH + CHG to two right - angles , ( a ) —AGH + BGH , ( † ) there- fore shall the angle CHG - BGH ; and ( c ) ... given any ways . Then because AB , MN are parallel , the angle BII will be ( a ) = LHI . Alfo becaufe KL and MN ...
... angle AGH + CHG to two right - angles , ( a ) —AGH + BGH , ( † ) there- fore shall the angle CHG - BGH ; and ( c ) ... given any ways . Then because AB , MN are parallel , the angle BII will be ( a ) = LHI . Alfo becaufe KL and MN ...
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Términos y frases comunes
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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.