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 sider |
Inni boken
Resultat 1-5 av 48
Side 36
... parallelogram , of which BC is a diameter ; the oppofite fides and angles of the figure are equal to one an- other ; and the diameter BC bifects it . Because AB is parallel to CD , A a and BC meets them , the alternate 29. 1. angles ABC ...
... parallelogram , of which BC is a diameter ; the oppofite fides and angles of the figure are equal to one an- other ; and the diameter BC bifects it . Because AB is parallel to CD , A a and BC meets them , the alternate 29. 1. angles ABC ...
Side 37
... parallelogram ABCD is equal to the parallelogram EBCF . Wherefore parallelograms , & c . Q E. D. P PROP . XXXVI . THEOR . ARALLELOGRAMS upon equal bafes , and between the fame parallels , are equal to one another . Let ABCD , EFGH be pa ...
... parallelogram ABCD is equal to the parallelogram EBCF . Wherefore parallelograms , & c . Q E. D. P PROP . XXXVI . THEOR . ARALLELOGRAMS upon equal bafes , and between the fame parallels , are equal to one another . Let ABCD , EFGH be pa ...
Side 38
... parallelogram : For the fame reafon , DBCF is a parallelogram : and EBCA is equal to DBCF , because they are upon the fame bafe BC , and between the fame parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA ...
... parallelogram : For the fame reafon , DBCF is a parallelogram : and EBCA is equal to DBCF , because they are upon the fame bafe BC , and between the fame parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA ...
Side 40
... parallelogram ABCD and the triangle EBC be upon the fame bafe BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC A a 37. 1. is equal a to the triangle EBC ...
... parallelogram ABCD and the triangle EBC be upon the fame bafe BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC A a 37. 1. is equal a to the triangle EBC ...
Side 41
... parallelogram FECG is likewife double f of the triangle AEC , becaufe it is upon the fame bafe , f 41. 1 . and between the fame parallels ; therefore the parallelogram FECG is equal to the triangle ABC : and it has one of its angles CEF ...
... parallelogram FECG is likewife double f of the triangle AEC , becaufe it is upon the fame bafe , f 41. 1 . and between the fame parallels ; therefore the parallelogram FECG is equal to the triangle ABC : and it has one of its angles CEF ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.