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 |
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Resultat 1-5 av 100
Side 15
... greater : It is required to cut off from AB , the greater , a part equal to C , the lefs . From the point A draw a the ftraight line AD equal to C ; and from the centre A , at the distance AD , describe b C JE B a 2. I. b 3. Poft , the ...
... greater : It is required to cut off from AB , the greater , a part equal to C , the lefs . From the point A draw a the ftraight line AD equal to C ; and from the centre A , at the distance AD , describe b C JE B a 2. I. b 3. Poft , the ...
Side 18
... greater ; which is abfurd . Therefore AB is not unequal to AC , that is , it is equal to it . b . 4. 1. Wherefore ... greater than the angle BCD ; therefore the angle ADC is greater alfo than BCD ; much more then is the angle BDC greater ...
... greater ; which is abfurd . Therefore AB is not unequal to AC , that is , it is equal to it . b . 4. 1. Wherefore ... greater than the angle BCD ; therefore the angle ADC is greater alfo than BCD ; much more then is the angle BDC greater ...
Side 24
... greater than either of the interior oppofite angles CBA , BAC . Bifecta AC in E , join BE , and produce it to F ... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be ...
... greater than either of the interior oppofite angles CBA , BAC . Bifecta AC in E , join BE , and produce it to F ... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be ...
Side 25
... greater fide of every triangle is oppofite to THE the greater angle . Let ABC be a triangle , of which the fide AC is greater than the fide AB ; the angle ABC is alfo greater than the angle BCA B A D a 3. 1 . Because AC is greater than ...
... greater fide of every triangle is oppofite to THE the greater angle . Let ABC be a triangle , of which the fide AC is greater than the fide AB ; the angle ABC is alfo greater than the angle BCA B A D a 3. 1 . Because AC is greater than ...
Side 26
... greater than the fide BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , and make a AD equal to AC ; and join DC . C Becaufe DA is equal to AC , the b 5. 1. angle ADC is likewise equal b to ACD ; but the ...
... greater than the fide BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , and make a AD equal to AC ; and join DC . C Becaufe DA is equal to AC , the b 5. 1. angle ADC is likewise equal b to ACD ; but the ...
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.