The Elements of Euclid: Viz. the First Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simson are Generally Adopted, But the Errors Overlooked by Him are Corrected, and the Obscurities of His and Other Editions Explained. Also Some of Euclid's Demonstrations are Restored, Others Made Shorter and More General, and Several Useful Propositions are Added. Together with Elements of Plane and Spherical Trigonometry, and a Treatise on Practical GeometryJ. Pillans & sons, 1799 - 351 σελίδες |
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Σελίδα 77
... opposite angles , & c . Q. E. D. c COR . If one of the fides DA be produced to E , the exterior angle EAB is equal to the interior oppofite angle BCD . For EAB , BAD are equal to two right angles ; that is , to the two angles BCD , BAD ...
... opposite angles , & c . Q. E. D. c COR . If one of the fides DA be produced to E , the exterior angle EAB is equal to the interior oppofite angle BCD . For EAB , BAD are equal to two right angles ; that is , to the two angles BCD , BAD ...
Σελίδα 141
... opposite to the homologous fides . Let the triangles ABC , DEF have their fides proportionals , fo that AB is to BC , as DE to EF ; and BC to CA , as EF to FD ; and confequently , by equality , BA to AC , as ED to DF ; the triangle ABC ...
... opposite to the homologous fides . Let the triangles ABC , DEF have their fides proportionals , fo that AB is to BC , as DE to EF ; and BC to CA , as EF to FD ; and confequently , by equality , BA to AC , as ED to DF ; the triangle ABC ...
Σελίδα 198
... , of which the base is the parallelogram ACBL , to which * The infifting ftraight lines are the fides of the parallelograms be- twixt the base and the opposite plane . 199 which OROP is the one oppofite , becaufe they 198 THE ELEMENTS.
... , of which the base is the parallelogram ACBL , to which * The infifting ftraight lines are the fides of the parallelograms be- twixt the base and the opposite plane . 199 which OROP is the one oppofite , becaufe they 198 THE ELEMENTS.
Σελίδα 231
... opposite to the right angle , be made the radius of a circle ; the other fides are the fines of the angles oppofite to them , or the colines of the angles adjacent to them . And if either of the fides about the right angle be made the ...
... opposite to the right angle , be made the radius of a circle ; the other fides are the fines of the angles oppofite to them , or the colines of the angles adjacent to them . And if either of the fides about the right angle be made the ...
Σελίδα 257
... opposite to it . Let ABC be a spherical triangle , having the right angle BAC ; as the fine of the fide AB to the radius , fo is the tan- gent of the fide AC to the tangent of the angle ABC . to Let D be the centre of the fphere , and ...
... opposite to it . Let ABC be a spherical triangle , having the right angle BAC ; as the fine of the fide AB to the radius , fo is the tan- gent of the fide AC to the tangent of the angle ABC . to Let D be the centre of the fphere , and ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifect Book XI cafe centre circle ABC circumference cofine confequently cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid exterior angle faid fame altitude fame manner fame multiple fame number fame ratio fame reaſon fecond fegment fhall fides fimilar firft firſt folid angle fome fore fquare fquare of AC fuperficies given ftraight line gnomon greater half the fum join lefs leſs Let ABC magnitudes meaſure oppofite angle pafs parallel parallelogram parallelopiped perpendicular plane angles prifm PROB propofition proportionals Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſhall ſquare tangent thefe THEOR theſe tiple triangle ABC Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 142 - 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 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Σελίδα 72 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Σελίδα 57 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Σελίδα 145 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Σελίδα 48 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.