Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Σελίδα 109
... Proportion is a Similitude or Likeness of Ra- tio's . Note , This Word would be better exprefs'd , by Proportionality , or Analogy , because by many it fignifies the fame as Ratio . V. Magnitudes are faid to have a Ratio to one another ...
... Proportion is a Similitude or Likeness of Ra- tio's . Note , This Word would be better exprefs'd , by Proportionality , or Analogy , because by many it fignifies the fame as Ratio . V. Magnitudes are faid to have a Ratio to one another ...
Σελίδα 110
... Proportion fhall be extended . A A A Duplicate Ratio is thus express'd twice . That is , the Ratio of A to C is the Duplicate of the Ratio of A to B , and triplicate Ratio'thus , D = 1 , thrice . That is , the Ratio of A to D , is ...
... Proportion fhall be extended . A A A Duplicate Ratio is thus express'd twice . That is , the Ratio of A to C is the Duplicate of the Ratio of A to B , and triplicate Ratio'thus , D = 1 , thrice . That is , the Ratio of A to D , is ...
Σελίδα 111
... Proportion ; and it fhall be in the first Order of Magnitudes , as the firft is to the laft , fo in the fecond Order of Magnitudes is the first first to the last or otherwise it is the Compari- Book IV . EUCLID'S Elements . III.
... Proportion ; and it fhall be in the first Order of Magnitudes , as the firft is to the laft , fo in the fecond Order of Magnitudes is the first first to the last or otherwise it is the Compari- Book IV . EUCLID'S Elements . III.
Σελίδα 112
... Proportion , is when , as the Antecedent is to the Confequent , fo is the An- tecedent to the Confequent ; and as the Confe- quent is to any other , fo is the Confequent to any other . As if A : B :: E : G. alfo B : C :: E : F. then by ...
... Proportion , is when , as the Antecedent is to the Confequent , fo is the An- tecedent to the Confequent ; and as the Confe- quent is to any other , fo is the Confequent to any other . As if A : B :: E : G. alfo B : C :: E : F. then by ...
Σελίδα 115
... Proportion to the Second B as the third C to the fourth D ; then alfo fball E , F the Equimultiples of the firft A and third C , have the fame Proportion to G , H , the Equimultiples of the fecond B and fourth D , according to any ...
... Proportion to the Second B as the third C to the fourth D ; then alfo fball E , F the Equimultiples of the firft A and third C , have the fame Proportion to G , H , the Equimultiples of the fecond B and fourth D , according to any ...
Συχνά εμφανιζόμενοι όροι και φράσεις
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe BC Baſe becauſe bifect Center Circ Cone confequently conft COROL Cylinder defcribed demonftrated Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples EUCLID's ELEMENTS faid fame Multiple fecond fhall fimilar fince firft folid fome fore four right ftanding given right Line gles Gnomon greater Hence infcribe leffer lefs likewife Line CD Magnitudes manifeft manner Number oppofite Paral parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular poffible Point Polyhedron Prifms Probl PROP Propofition Pyramids Ratio Rectangle right Angles right Line AB right Line AC right-lined Figure SCHOL SCHOLIU Segment ſhall Side BC Sphere Square thefe thofe thro tiple Triangle ABC Whence whofe whole
Δημοφιλή αποσπάσματα
Σελίδα 31 - 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 145 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Σελίδα 33 - ABD, is equal* to two right angles, «13. 1. therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are sides of the figure; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles; therefore all the exterior angles are equal to four right angles.
Σελίδα 27 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Σελίδα 31 - The three angles of any triangle taken together are equal to the three angles of any other triangle taken together. From whence it follows, 2.
Σελίδα 11 - That a straight line may be drawn from any point to any other point. 2. That a straight line may be produced to any length in a straight line.