Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Σελίδα 10
... fimilar . Moreover , Magnitudes are faid to agree , or coincide , when the parts of the one being ap- ply'd to the parts of the other , they fill up an equal , or the fame Space . 9. Every Whole is greater than its Part . 10. Two right ...
... fimilar . Moreover , Magnitudes are faid to agree , or coincide , when the parts of the one being ap- ply'd to the parts of the other , they fill up an equal , or the fame Space . 9. Every Whole is greater than its Part . 10. Two right ...
Σελίδα 77
... fimilar and unequal Segments ABC , ADC , of two Circles , cannot be fet upon the fame right Line AC on the fame Side there- of . a b C d 22.3 . Hyp . 3.ax. 21. I For . For if they are faid to be fimilar , Book III . 77 EUCLID'S Elements .
... fimilar and unequal Segments ABC , ADC , of two Circles , cannot be fet upon the fame right Line AC on the fame Side there- of . a b C d 22.3 . Hyp . 3.ax. 21. I For . For if they are faid to be fimilar , Book III . 77 EUCLID'S Elements .
Σελίδα 78
Euclid . For if they are faid to be fimilar , draw CB cutting the Circumference in B and D ; and join AD , and AB . Now because the Segments Def . 10. are fuppos'd to be fimilar , the Ang . ADC = ABC . Which is abfurd . 3 . 16.1 . PROP ...
Euclid . For if they are faid to be fimilar , draw CB cutting the Circumference in B and D ; and join AD , and AB . Now because the Segments Def . 10. are fuppos'd to be fimilar , the Ang . ADC = ABC . Which is abfurd . 3 . 16.1 . PROP ...
Σελίδα 125
... fimilar Proportionals be taken from fimilar Proportionals , the remainders fhall be Proportional . 2. Hence alfo is converfe Ratio demonftrated . : e g 17. 5 . byp . & 11. 5 . For let AB CB :: DE : FE . then fhall AB : AC :: DE : DF ...
... fimilar Proportionals be taken from fimilar Proportionals , the remainders fhall be Proportional . 2. Hence alfo is converfe Ratio demonftrated . : e g 17. 5 . byp . & 11. 5 . For let AB CB :: DE : FE . then fhall AB : AC :: DE : DF ...
Σελίδα 136
... fimilar to the whole one FBE . PROP . V. If the Sides of two Triangles ABC , DEF , are proportional , viz . AB : BC :: DE : EF . and AC : BC : DF : EF . alfo AB AC :: DE : DF . the faid Triangles are Equiangular , and their Angles un ...
... fimilar to the whole one FBE . PROP . V. If the Sides of two Triangles ABC , DEF , are proportional , viz . AB : BC :: DE : EF . and AC : BC : DF : EF . alfo AB AC :: DE : DF . the faid Triangles are Equiangular , and their Angles un ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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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.