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 |
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Seite v
... for , in other cases , two folid figures may be contained by similar planes of the fame number and magnitude , and yet be unequal to one another ; as shall be made evident in the Notes subjoined to these Elements .
... for , in other cases , two folid figures may be contained by similar planes of the fame number and magnitude , and yet be unequal to one another ; as shall be made evident in the Notes subjoined to these Elements .
Seite vi
7 + T I 1 of this Book depend the 25th and 28th Propofitions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31st , 320 , 33d , 34th , 36th , 37th , and 40th of the fame Book ; and the 12th of the 12th Book ...
7 + T I 1 of this Book depend the 25th and 28th Propofitions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31st , 320 , 33d , 34th , 36th , 37th , and 40th of the fame Book ; and the 12th of the 12th Book ...
Seite 13
Things which are double of the fame , are equal to one another , VII . Things which are halves of the fame , are equal to one another , VIII . Magnitudes which coincide with one another , that is , which exactly fill ...
Things which are double of the fame , are equal to one another , VII . Things which are halves of the fame , are equal to one another , VIII . Magnitudes which coincide with one another , that is , which exactly fill ...
Seite 15
Ax . But it has been shewn , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the fame , are equal to one another ; therefore the straight line AL is equal to BC .
Ax . But it has been shewn , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the fame , are equal to one another ; therefore the straight line AL is equal to BC .
Seite 26
... c fide is opposite to the greater angle ; therefore the fide DB is greater than the side BC ; but DỄ is equal to BA and AC ; therefore the sides BA , AC are greater than BC . In the fame In the fame manner , it may be demonstrated , ...
... c fide is opposite to the greater angle ; therefore the fide DB is greater than the side BC ; but DỄ is equal to BA and AC ; therefore the sides BA , AC are greater than BC . In the fame In the fame manner , it may be demonstrated , ...
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ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſect Book caſe centre circle circumference common cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples fall fame fides figure firſt folid fore four fourth greater half inches join leſs Let ABC magnitudes mean meaſure meet oppoſite parallel parallelogram parallelopiped paſs perpendicular plane priſm PROB produced PROP proportionals propoſition proved pyramid radius ratio rectangle contained rectilineal remaining right angles ſame ſame manner ſame multiple ſame reaſon ſecond ſegment ſhall ſides ſimilar ſolid ſquare ſtraight line ſum taken tangent THEOR theſe third touches triangle triangle ABC twice uſe Wherefore whole
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.
Bibliografische Informationen
| Titel | 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 ... |
| Autor/in | Alexander Ingram |
| Verlag | J. Pillans & sons, 1799 |
| Original von | University of Michigan |
| Digitalisiert | 8. Juni 2007 |
| Länge | 351 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |