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 Geometry |
From inside the book
Results 1-5 of 75
Page 8
... PROB . IX . in p . 320. there is ADE , instead of ADB , and Pl . I. Fig . 16. is omitted in the margin oppofite to PROB . X .; and in p . 325. in the first line of the last column of the Table , there is 13 , inftead of 18 . 1 THE ...
... PROB . IX . in p . 320. there is ADE , instead of ADB , and Pl . I. Fig . 16. is omitted in the margin oppofite to PROB . X .; and in p . 325. in the first line of the last column of the Table , there is 13 , inftead of 18 . 1 THE ...
Page 14
... PROB . ROM a given point to draw a ftraight line equal to a given itraight line . Let A be the given point , and BC the given straight line ; it is required to draw from the point A a straight line equal to BC . From the point A to B ...
... PROB . ROM a given point to draw a ftraight line equal to a given itraight line . Let A be the given point , and BC the given straight line ; it is required to draw from the point A a straight line equal to BC . From the point A to B ...
Page 15
... PROB . ROM the greater of two given ftraight lines to cut off a part equal to the lefs . FR Let AB and C be the two given ftraight lines , whereof AB is the greater : It is required to cut off from AB , the greater , a part equal to C ...
... PROB . ROM the greater of two given ftraight lines to cut off a part equal to the lefs . FR Let AB and C be the two given ftraight lines , whereof AB is the greater : It is required to cut off from AB , the greater , a part equal to C ...
Page 19
... PROB . O bifect a given rectilineal angle , that is , to divide it into two equal angles . Tit Let BAC be the given rectilineal angle , it is required to bi- fect it . C 2 Take BOOK I. a Take any point D in AB , OF EUCLID . 19.
... PROB . O bifect a given rectilineal angle , that is , to divide it into two equal angles . Tit Let BAC be the given rectilineal angle , it is required to bi- fect it . C 2 Take BOOK I. a Take any point D in AB , OF EUCLID . 19.
Page 20
... PROB . O bifect a given finite ftraight line , that is , to di- vide it into two equal parts . Let AB be the given ftraight line ; it is required to divide it into two equal parts . Defcribe a upon it an equilateral triangle ABC , and ...
... PROB . O bifect a given finite ftraight line , that is , to di- vide it into two equal parts . Let AB be the given ftraight line ; it is required to divide it into two equal parts . Defcribe a upon it an equilateral triangle ABC , and ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.