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 Seiten |
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Seite 110
... same ratio to the fecond which the third has to the fourth , when as many times as any multiple of the first contains the second , so many times does the fame multiple of the third contain the fourth . VI . Magnitudes which have the same ...
... same ratio to the fecond which the third has to the fourth , when as many times as any multiple of the first contains the second , so many times does the fame multiple of the third contain the fourth . VI . Magnitudes which have the same ...
Seite 119
... multiple of BC contains D ; therefore AB has to D Book V. a greater ratio than BC has to D. Alfo D has to BC a greater ratio than it has to AB . For , b7 . def . 5 . having made the same construction , take also MD the least mul- tiple ...
... multiple of BC contains D ; therefore AB has to D Book V. a greater ratio than BC has to D. Alfo D has to BC a greater ratio than it has to AB . For , b7 . def . 5 . having made the same construction , take also MD the least mul- tiple ...
Seite 125
... multiple of the whole AB , that MN is of BE ; the remainder NA is the fame multiple of the remainder AE , that the ... same number of times B that the whole MC contains DF : and MA , MC E are any equimultiples of AB , CD ; as many times , ...
... multiple of the whole AB , that MN is of BE ; the remainder NA is the fame multiple of the remainder AE , that the ... same number of times B that the whole MC contains DF : and MA , MC E are any equimultiples of AB , CD ; as many times , ...
Seite 164
... , a 27. 3. KGL are alfo all equal ; therefore the arch BL is the same multiple of the arch BC , that the angle BGL is of the angle BGC . Take , in like manner , the arch EM the leaft multiple of A D M L G H · a 27. 3 164 THE ELEMENTS.
... , a 27. 3. KGL are alfo all equal ; therefore the arch BL is the same multiple of the arch BC , that the angle BGL is of the angle BGC . Take , in like manner , the arch EM the leaft multiple of A D M L G H · a 27. 3 164 THE ELEMENTS.
Seite 213
... same point , to touch the circle in the extremities of the arch . IF PROP . I. THEOR * . from the greater of two ... multiple be greater * This is Prop . I. Book X. of Euclid . A D F Book XII . greater than AB , THE ...
... same point , to touch the circle in the extremities of the arch . IF PROP . I. THEOR * . from the greater of two ... multiple be greater * This is Prop . I. Book X. of Euclid . A D F Book XII . greater than AB , THE ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.