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 iv
... Book , in place of the legitimate one which Euclid had given ; and by taking out of this Book , befides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an abfurd one in place of it ...
... Book , in place of the legitimate one which Euclid had given ; and by taking out of this Book , befides other things , the good Definition which Eudoxus or Euclid had given of Compound Ratio , and giving an abfurd one in place of it ...
Σελίδα v
... Book , there is this , which is the 10th , viz . " Equal and fimilar folid 66 46 Figures are those which are contained by fimilar Planes of the fame number and magnitude . " Now , this Propofition is a Theorem , not a De- finition ...
... Book , there is this , which is the 10th , viz . " Equal and fimilar folid 66 46 Figures are those which are contained by fimilar Planes of the fame number and magnitude . " Now , this Propofition is a Theorem , not a De- finition ...
Σελίδα vi
... Book depend the 25th and 28th Propofi → tions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31ft , 32d , 33d , 34th , 36th , 37th , and 40th of the fame Book ; and the 12th of the 12th Book depends upon the ...
... Book depend the 25th and 28th Propofi → tions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31ft , 32d , 33d , 34th , 36th , 37th , and 40th of the fame Book ; and the 12th of the 12th Book depends upon the ...
Σελίδα 2
... Book , but he did not take notice , that the alteration he complains of there , is only one of a series of alterations made in every Pro- pofition from the 9th to it ; and in the fame manner , when he corrected the 5th Propofition of ...
... Book , but he did not take notice , that the alteration he complains of there , is only one of a series of alterations made in every Pro- pofition from the 9th to it ; and in the fame manner , when he corrected the 5th Propofition of ...
Σελίδα 3
... Book , however , the change of expreffion made in the Definitions , caufes a fimilar change in their application , on which account , in the Demonftrations , there is fometimes a different ftep neceffary in order to connect them with ...
... Book , however , the change of expreffion made in the Definitions , caufes a fimilar change in their application , on which account , in the Demonftrations , there is fometimes a different ftep neceffary in order to connect them with ...
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.