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 ...W. Strahan, 1782 - 399 páginas |
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Página 118
... exceed one another . · V. Magnitudes are faid to be in the fame Ratio , the first to the second , and the third to the fourth ; when the Equimultiples of the first and third , compared with the Equimultiples of the fecond and fourth ...
... exceed one another . · V. Magnitudes are faid to be in the fame Ratio , the first to the second , and the third to the fourth ; when the Equimultiples of the first and third , compared with the Equimultiples of the fecond and fourth ...
Página 121
... exceeds the Multiple of the fecond , but the Multiple of the third does not exceed the Mul- tiple of the fourth then the first to the fecond is faid to have a greater Proportion than the third to the fourth . VIII . Analogy is a ...
... exceeds the Multiple of the fecond , but the Multiple of the third does not exceed the Mul- tiple of the fourth then the first to the fecond is faid to have a greater Proportion than the third to the fourth . VIII . Analogy is a ...
Página 126
... exceeds + Def . 5 of M , then + L will exceed N ; if K be equal to M , L will be equal to N ; and if K is lefs than M , then L will be less than N : But K and Lare Equimultiples of E and F , alfo M and N are Equimulti- ples of G and H ...
... exceeds + Def . 5 of M , then + L will exceed N ; if K be equal to M , L will be equal to N ; and if K is lefs than M , then L will be less than N : But K and Lare Equimultiples of E and F , alfo M and N are Equimulti- ples of G and H ...
Página 127
... exceeds M , then L will exceed N ; and if K be equal to M , L will be equal to N ; and if K be less than M , L will be lefs than N : It is manifeft , likewise , if M exceeds K , that N fhall exceed L ; if equal , equal ; but if lefs ...
... exceeds M , then L will exceed N ; and if K be equal to M , L will be equal to N ; and if K be less than M , L will be lefs than N : It is manifeft , likewise , if M exceeds K , that N fhall exceed L ; if equal , equal ; but if lefs ...
Página 129
... exceeds F , then E will exceed F ; if D be equal to F , E will be equal to F ; and if lefs , lefs . But D and E are Equimultiples of A and B ; and F is any other Multiple of C. Therefore it will be as A is Def . 5 . to C , fo is B to C ...
... exceeds F , then E will exceed F ; if D be equal to F , E will be equal to F ; and if lefs , lefs . But D and E are Equimultiples of A and B ; and F is any other Multiple of C. Therefore it will be as A is Def . 5 . to C , fo is B to C ...
Términos y frases comunes
ABCD adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle A B C Circumference Cofine Cone confequently Cylinder defcribed demonftrated Diameter Diſtance drawn equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft folid Parallelopipedon fome fore ftand fubtending given Right Line Gnomon join leffer lefs likewife Logarithm Magnitudes Meaſure Number parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment Semicircle ſhall Sides A B Sine Solid Sphere Square Subtangent thefe THEOREM thofe thro tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.