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 páginas |
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Página 16
... straight line AB upon DE , the point B fhall coincide with the point E , becaufe AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore alfo the point C ...
... straight line AB upon DE , the point B fhall coincide with the point E , becaufe AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore alfo the point C ...
Página 21
... line makes with another straight line , are equal to one another , each of them is called a right d angle ; therefore each of the angles DCF , ECF is a right angle . Wherefore , from the given point C , in the given ftraight line AB ...
... line makes with another straight line , are equal to one another , each of them is called a right d angle ; therefore each of the angles DCF , ECF is a right angle . Wherefore , from the given point C , in the given ftraight line AB ...
Página 22
... line , & c . Q. E. D. d 1 . a 13. I. PROP . XIV . THEOR . TF , at a point in a ftraight line , two other ftraight lines , upon the oppofite fides of it , make the ad- jacent angles together equal to two right angles , these two straight ...
... line , & c . Q. E. D. d 1 . a 13. I. PROP . XIV . THEOR . TF , at a point in a ftraight line , two other ftraight lines , upon the oppofite fides of it , make the ad- jacent angles together equal to two right angles , these two straight ...
Página 23
... line with BC . And , in like manner , it may be demonftrated , that no other can be in the fame ftraight line with ... straight line DE makes with AB the angles AED , DEB , thefe alfo are together equal a to two right angles ; and CEA ...
... line with BC . And , in like manner , it may be demonftrated , that no other can be in the fame ftraight line with ... straight line DE makes with AB the angles AED , DEB , thefe alfo are together equal a to two right angles ; and CEA ...
Página 27
... straight lines A , B , C. C a 20. I. a 3. t . b 3. Poft . Because the point F is the centre of the circle DKL , FD is equal to FK ; but FD is equal to the ftraight line A ; there- c 15. Def . fore FK is equal to A : Again , because G is ...
... straight lines A , B , C. C a 20. I. a 3. t . b 3. Poft . Because the point F is the centre of the circle DKL , FD is equal to FK ; but FD is equal to the ftraight line A ; there- c 15. Def . fore FK is equal to A : Again , because G is ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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...
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.