The first and second books of Euclid explained to beginners, by C.P. Mason |
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Σελίδα 18
... taken from the equals , DE and DF , the remainders , CE and AF , will be equal . ( Axiom III . ) The lines , CB and CE , are equal , being radii of the same circle . So that the lines CB and A F are both equal to the line CE . Therefore ...
... taken from the equals , DE and DF , the remainders , CE and AF , will be equal . ( Axiom III . ) The lines , CB and CE , are equal , being radii of the same circle . So that the lines CB and A F are both equal to the line CE . Therefore ...
Σελίδα 20
... taken not to use the same letters to mark the different points of the figure . PROPOSITION III . From the greater of two given straight lines , to cut off a part equal to the less . To do this we must be able , - 1. From a given point ...
... taken not to use the same letters to mark the different points of the figure . PROPOSITION III . From the greater of two given straight lines , to cut off a part equal to the less . To do this we must be able , - 1. From a given point ...
Σελίδα 26
... taken from equals , the re- mainders are equal . ( Ax . III . ) 2. That if two As have two sides of the one equal to two sides of the other , each to each , and have likewise the s contained by these two pairs of sides equal , then the ...
... taken from equals , the re- mainders are equal . ( Ax . III . ) 2. That if two As have two sides of the one equal to two sides of the other , each to each , and have likewise the s contained by these two pairs of sides equal , then the ...
Σελίδα 28
... taken away , the re- mainders , namely the s B A C and B CA , will be equal to each other ( Ax . 3 ) . But these are the s opposite the equal sides of the isosceles △ A B. C. Therefore the first part of the proposition has been proved ...
... taken away , the re- mainders , namely the s B A C and B CA , will be equal to each other ( Ax . 3 ) . But these are the s opposite the equal sides of the isosceles △ A B. C. Therefore the first part of the proposition has been proved ...
Σελίδα 39
... taken from them ( as in Fig . 2 ) , the sums or differences ACB and A F B will be equal . ( If the line C F passes through the point B , it follows immediately that the s A C B and A F B ( i . e . , D F E ) are equal , as in that case ...
... taken from them ( as in Fig . 2 ) , the sums or differences ACB and A F B will be equal . ( If the line C F passes through the point B , it follows immediately that the s A C B and A F B ( i . e . , D F E ) are equal , as in that case ...
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The First and Second Books of Euclid Explained to Beginners, by C.P. Mason Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B and CD A B is equal AC and CB Æneid axiom beginner bisected centre Consequently diagonal draw a straight Edition equal in area equal respectively equal to twice equilateral Euclid exterior exterior angle Fcap figure finite right line follows formed fourth proposition given finite right given line given point given rectilineal given straight line gnomon Grammar greater half a right hypotenuse interior and opposite isosceles Join the points join two given Latin length less line A B line CB linear units lines are parallel magnitudes meeting the line opposite sides parallelogram point F proof Prop proposition prove this proposition rectangle contained right angles side A C straight line meets suppose three sides triangle unequal