The Elements of Euclid |
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Side 120
Magnitudes which have the same ratio are called proportionals . N. B. " When
four magnitudes are proportionals , it is usually expressed by saying , the first is
to the se• cond , as the third to the fourth . ” VII . When of the equimultiples of four
...
Magnitudes which have the same ratio are called proportionals . N. B. " When
four magnitudes are proportionals , it is usually expressed by saying , the first is
to the se• cond , as the third to the fourth . ” VII . When of the equimultiples of four
...
Side 121
In proportionals , the antecedent terms are called homologous to one another , as
also the consequents to one anothier . Geometers make use of the following
technical words to sig . nify certain ways of changing either the order or
magnitude ...
In proportionals , the antecedent terms are called homologous to one another , as
also the consequents to one anothier . Geometers make use of the following
technical words to sig . nify certain ways of changing either the order or
magnitude ...
Side 122
Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is
any number of magnitudes more than two , and as many others , so that they are
proportionals when taken two and two of each rank , and it is inferred , that the ...
Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is
any number of magnitudes more than two , and as many others , so that they are
proportionals when taken two and two of each rank , and it is inferred , that the ...
Side 129
... equal to the second , or less than it , the third can be proved to be equal to the
fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . IF
four magnitudes be proportionals , they are pro- See Note . portionals also when
...
... equal to the second , or less than it , the third can be proved to be equal to the
fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . IF
four magnitudes be proportionals , they are pro- See Note . portionals also when
...
Side 136
... if less , less : and G , K are any equimultiples whatever of A , E , and L , N any
whatever of B , F : therefore , as A is to B , so is E to Fa . Wherefore ratios that , & c
. Q.F.D. 534 PROP . XII . THEOR . IF any number of magnitudes be proportionals
...
... if less , less : and G , K are any equimultiples whatever of A , E , and L , N any
whatever of B , F : therefore , as A is to B , so is E to Fa . Wherefore ratios that , & c
. Q.F.D. 534 PROP . XII . THEOR . IF any number of magnitudes be proportionals
...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |
Vanlige uttrykk og setninger
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Bibliografisk informasjon
| Tittel | The Elements of Euclid |
| Forfattere | Euclid, Robert Simson |
| Redaktør | Robert Simson |
| Utgiver | Johnson and Warner, 1811 |
| Original fra | University of Chicago |
| Digitalisert | 17. jun 2013 |
| Lengde | 518 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |