The First Book of Euclid's Elements, Simplified, Explained, and Illustrated for the Use of Beginners. ... By W. Trollope1847 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 13
... BC = BA ( Def . 15 ) . 3. Hence AC and BC are each to AB . = 4. But things which the same thing , are = to one ... base , or under side , longer than either of the two equal sides AC , AF , and BC , BF . A more general proposition than ...
... BC = BA ( Def . 15 ) . 3. Hence AC and BC are each to AB . = 4. But things which the same thing , are = to one ... base , or under side , longer than either of the two equal sides AC , AF , and BC , BF . A more general proposition than ...
Σελίδα 18
... base BC shall = base EF ; and the area of the △ ABC shall area of a DEF ; also the △ ABC shall B E H P = DEF ; another ACB shall = dfe . DEMONST . - 1 . For if the ABC be applied to the △ DEF , so that the pt . A may be on D , and ...
... base BC shall = base EF ; and the area of the △ ABC shall area of a DEF ; also the △ ABC shall B E H P = DEF ; another ACB shall = dfe . DEMONST . - 1 . For if the ABC be applied to the △ DEF , so that the pt . A may be on D , and ...
Σελίδα 19
coincide with the pt . E , the base BC must coincide with the base EF ; because , the pts . B and c coinciding respectively with E and F , if the base BC does not coincide with the base EF , but lies above or below it , two straight ...
coincide with the pt . E , the base BC must coincide with the base EF ; because , the pts . B and c coinciding respectively with E and F , if the base BC does not coincide with the base EF , but lies above or below it , two straight ...
Σελίδα 21
... base . Therefore the s at the base , & c . - Q . E. D. COROLLARY . - Hence every equilateral △ is also equiangular ... BC , ... △ BAC ACB ; .. the ABC , ACB , BAC , are equal : i.e. the ABC is equiangular . — Q . E. D. 8 Thus : - : - A ...
... base . Therefore the s at the base , & c . - Q . E. D. COROLLARY . - Hence every equilateral △ is also equiangular ... BC , ... △ BAC ACB ; .. the ABC , ACB , BAC , are equal : i.e. the ABC is equiangular . — Q . E. D. 8 Thus : - : - A ...
Σελίδα 23
Since in S DBC , ACB , the side DB = AC , and BC is common to both , .. the two DB , BC = the two AC , CB , each to each ; and the DBC = ACB ( Hyp . ) ; .. base DC = base AB , and the area of △ DBC area of A ACB : i . e . the ...
Since in S DBC , ACB , the side DB = AC , and BC is common to both , .. the two DB , BC = the two AC , CB , each to each ; and the DBC = ACB ( Hyp . ) ; .. base DC = base AB , and the area of △ DBC area of A ACB : i . e . the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angle contained base BC bisect CD Prop coincide Const CONST.-In CONST.-Join CONST.-Let DEMONST.-Because DEMONST.-For demonstration diam diameter draw EBCF ENUN ENUN.-If ENUN.-Let ABC ENUN.-To equal sides equilateral Euclid EUCLID'S ELEMENTS exterior four rt given point given straight line interior and opposite interior opposite isosceles join Let ABC line be drawn line drawn meet opposite angles opposite sides parallel parallelogram perpendicular Post PROB produced Proposition proved rectilineal figure rhombus right angles side BC square take any pt THEOR THEOR.-If Theorem trapezium trapezium ABCD vertical Wherefore XXIX XXXI XXXII XXXIV