Elements of Geometry, Containing the First Six Books of Euclid |
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Seite v
In the selection , the Editor has taken some from Cress- well , Bland , & c . and added others of his own ; and he trusts it is made so as to meet the approbation of the public in general . There are also algebraic demonstrations ...
In the selection , the Editor has taken some from Cress- well , Bland , & c . and added others of his own ; and he trusts it is made so as to meet the approbation of the public in general . There are also algebraic demonstrations ...
Seite xviii
However , Syracuse was at length taken ; " what gave Marcellus the greatest concern , " says Plu- tarch , " was the unhappy fate of Archimedes , who was at that time in the museum ; so intent was his mind , as well as his eye ...
However , Syracuse was at length taken ; " what gave Marcellus the greatest concern , " says Plu- tarch , " was the unhappy fate of Archimedes , who was at that time in the museum ; so intent was his mind , as well as his eye ...
Seite xxvi
... so very nervous and elegant , as not to be equalled by any geometrical writer , ancient or modern ; and his method is such that nothing is taken as true unless demonstrated ; and nothing is demonstrated , but from what went before .
... so very nervous and elegant , as not to be equalled by any geometrical writer , ancient or modern ; and his method is such that nothing is taken as true unless demonstrated ; and nothing is demonstrated , but from what went before .
Seite 4
If equals be taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are double of the same ...
If equals be taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are double of the same ...
Seite 10
A But if the point D be taken in either of them , AC , BC , the proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this ...
A But if the point D be taken in either of them , AC , BC , the proposition is manifest ; for so the whole ac would be equal to its part AD , or the whole BC equal to its part BD , which is impossible . Dr. Simson , in his note to this ...
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ABC is equal ABCD alternate angle ABC angle ACB angle BAC angles equal applied base base BC bisected centre circle ABC circumference common consequently demonstrated described diameter divided double draw equal equal angles equiangular equilateral equimultiples exceed extreme fall figure fore four fourth Geometry given circle given rectilineal given right line greater half hence inscribed join less Let ABC magnitudes manner mean meet multiple opposite parallel parallelogram pass perpendicular PROBLEM produced proportional PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles right line AC sector segment shown sides similar square taken THEOREM third triangle ABC whence Wherefore whole
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Seite xxiv - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Seite 72 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 31 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Seite 146 - 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 25 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Seite 6 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Seite 71 - DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Seite 97 - To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. . Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, • 17.3. C, D, draw...
Seite 5 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Seite 86 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.