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 σελίδες |
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Σελίδα 118
... Ratio is a certain mutual Habitude of Mag- nitudes of the fame Kind , according to Quan- tity . IV . Magnitudes are faid to have Proportion to each other , which being multiplied , can exceed one another . · V. Magnitudes are faid to be ...
... Ratio is a certain mutual Habitude of Mag- nitudes of the fame Kind , according to Quan- tity . IV . Magnitudes are faid to have Proportion to each other , which being multiplied , can exceed one another . · V. Magnitudes are faid to be ...
Σελίδα 119
... Ratio , according to the Conditions that Magnitudes in the fame Ratio muft have according to the fifth Definition ; and let the firft be a Multiple of the fecond : I fay , the third is alfo the fame Mul- tiple of the fourth . For ...
... Ratio , according to the Conditions that Magnitudes in the fame Ratio muft have according to the fifth Definition ; and let the firft be a Multiple of the fecond : I fay , the third is alfo the fame Mul- tiple of the fourth . For ...
Σελίδα 121
... Ratio to what it has to the fecond . XI . But when four Magnitudes are continued Proportionals , the first shall have a triplicate Ratio to the fourth of what it has to the fe- cond ; and fo always one more in Order , as the ...
... Ratio to what it has to the fecond . XI . But when four Magnitudes are continued Proportionals , the first shall have a triplicate Ratio to the fourth of what it has to the fe- cond ; and fo always one more in Order , as the ...
Σελίδα 131
... Ratio Def . 7 . to D , than C has to D. I fay , moreover , that D has a greater Ratio to C than it has to A B : For the fame Conftruction remaining , we demonftrate , as be- fore , that N exceeds K , but not FH . And N is a Multiple of ...
... Ratio Def . 7 . to D , than C has to D. I fay , moreover , that D has a greater Ratio to C than it has to A B : For the fame Conftruction remaining , we demonftrate , as be- fore , that N exceeds K , but not FH . And N is a Multiple of ...
Σελίδα 141
... Ratio . The Demonftration of converfe Ratio , laid down in this Corollary , is only particular . For Alternation ( which is used herein ) cannot be applied but when the four proportional Magnitudes are all of the fame Kind , as will ...
... Ratio . The Demonftration of converfe Ratio , laid down in this Corollary , is only particular . For Alternation ( which is used herein ) cannot be applied but when the four proportional Magnitudes are all of the fame Kind , as will ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.