Euclid's Elements of Geometry: From the Latin Translation of Commandine, to which is Added, a Treatise of the Nature and Arithmetic of Logarithms ; Likewise Another of the Elements of Plane and Spherical Trigonometry ; with a Preface ... |
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Resultat 1-5 av 7
Side 119
That is , if there be four Magnitudes , and you take any Equimultiples of the firft
and third , and also any Equimultiples of the second and fourth ; and if the
Multiple of the first be greater than the Multiple of the second ; and also the
Multiple of the ...
That is , if there be four Magnitudes , and you take any Equimultiples of the firft
and third , and also any Equimultiples of the second and fourth ; and if the
Multiple of the first be greater than the Multiple of the second ; and also the
Multiple of the ...
Side 124
If the first be the fame Multiple of the second , as the third is of the fourth ; and if
the fifth be the same Multiple of the second , as the fixth is of the fourth ; then all
the first , added to the fifth , be the same Multiple of the second , as the third ,
added ...
If the first be the fame Multiple of the second , as the third is of the fourth ; and if
the fifth be the same Multiple of the second , as the fixth is of the fourth ; then all
the first , added to the fifth , be the same Multiple of the second , as the third ,
added ...
Side 125
If the first be the same Multiple of the second , as the third is of ibe fourth , and
there be taken Equ multiples of the first and third ; then will the Magnitudes so
taken be Equimultiples of the second and fourib . L ET the first A be the same
Multiple ...
If the first be the same Multiple of the second , as the third is of ibe fourth , and
there be taken Equ multiples of the first and third ; then will the Magnitudes so
taken be Equimultiples of the second and fourib . L ET the first A be the same
Multiple ...
Side 128
And then , because A E is the same Multiple of CF , as E B is of CG , and CG is
equal to DF ; A E fhall be the same Multiple of CF , as E B is of F D. But A E is put
the same Multiple of CF , as AB is of CD . Therefore E B is the same Multiple of
F D ...
And then , because A E is the same Multiple of CF , as E B is of CG , and CG is
equal to DF ; A E fhall be the same Multiple of CF , as E B is of F D. But A E is put
the same Multiple of CF , as AB is of CD . Therefore E B is the same Multiple of
F D ...
Side 139
K + Р Because GH is the fame Multiple of A E , as HK is of B EB ; therefore GH * is
the 1 D same Multiple of AE as GK } H is of A B. But GH is the E + FIMI fame
Multiple of A E , as L M is of CF. Wherefore GK is G А the fame Multiple of A B , as
...
K + Р Because GH is the fame Multiple of A E , as HK is of B EB ; therefore GH * is
the 1 D same Multiple of AE as GK } H is of A B. But GH is the E + FIMI fame
Multiple of A E , as L M is of CF. Wherefore GK is G А the fame Multiple of A B , as
...
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Vanlige uttrykk og setninger
A B C ABCD added alſo Altitude Bale Baſe becauſe Centre Circle Circumference common Cone conſequently contained Cylinder demonſtrated deſcribed Diameter Difference Diſtance divided double draw drawn equal equal Angles equiangular exceeds fall fame fince firſt fore four fourth given greater half ibis join leſs likewiſe Logarithm Magnitudes manner Multiple Number oppoſite parallel Parallelogram perpendicular Place Plane Point Polygon Priſm produced Prop Proportion PROPOSITION proved Pyramid Quadrant Ratio Reaſon Rectangle remaining Right Angles Right Line Right Line A B ſaid ſame ſay ſecond Segment Series ſhall ſhall be equal Sides ſimilar ſince Sine Solid ſome Sphere Square taken tbis Terms THEOREM thereof theſe third thoſe thro touch Triangle Unity Whence Wherefore whole whoſe Baſe
Populære avsnitt
Side 193 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side xxiii - If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases, or third sides, equal; and the two triangles shall be equal; and their other angles shall be equal, each to each, viz. those to which the equal sides are opposite.
Side 236 - 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 11 - ... sides 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...
Side 85 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Side 147 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Side 50 - CB, and to twice the rectangle AC, CB: but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB ; therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c.
Side xxv - EF (Hyp.), the two sides GB, BC are equal to the two sides DE, EF, each to each. And the angle GBC is equal to the angle DEF (Hyp.); Therefore the base GC is equal to the base DF (I.
Side xxxiv - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other (26.
Side 194 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.
Bibliografisk informasjon
| Tittel | Euclid's Elements of Geometry: From the Latin Translation of Commandine, to which is Added, a Treatise of the Nature and Arithmetic of Logarithms ; Likewise Another of the Elements of Plane and Spherical Trigonometry ; with a Preface ... |
| Forfatter | John Keill |
| Redaktør | Mr. Cunn (Samuel) |
| Utgave | 12 |
| Utgiver | W. Strahan, 1782 |
| Original fra | University of Michigan |
| Digitalisert | 8. jun 2007 |
| Lengde | 399 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |