Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |
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Σελίδα vi
... on the whole being turned about the two centres of the spheres , will describe a
surface in which any two points being taken , the straight line between them , with
its prolongation either way , may be proved to lie wholly in that surface .
... on the whole being turned about the two centres of the spheres , will describe a
surface in which any two points being taken , the straight line between them , with
its prolongation either way , may be proved to lie wholly in that surface .
Σελίδα viii
On the whole therefore it may be an interesting question in what place a
geometer would be warranted in saying , ' I could have proved these
preliminaries , but it would have been necessary to disturb the order which
directs that lines be ...
On the whole therefore it may be an interesting question in what place a
geometer would be warranted in saying , ' I could have proved these
preliminaries , but it would have been necessary to disturb the order which
directs that lines be ...
Σελίδα 6
... A and B would coincide with one another ; wherefore A and + 1.Nom . 14. B are
equal t . And in the same manner if the magnitudes equal to C were more than
two . And by parity of reasoning , the like may be proved in every other instance .
... A and B would coincide with one another ; wherefore A and + 1.Nom . 14. B are
equal t . And in the same manner if the magnitudes equal to C were more than
two . And by parity of reasoning , the like may be proved in every other instance .
Σελίδα 7
than C ; therefore ( as has been proved above ) A also is greater than C ; that is ,
C is less than A. And in a similar manner if C were greater than B. CoR . 3.
Magnitudes which are equal to equals , are equal to one another . Let A be equal
to B ...
than C ; therefore ( as has been proved above ) A also is greater than C ; that is ,
C is less than A. And in a similar manner if C were greater than B. CoR . 3.
Magnitudes which are equal to equals , are equal to one another . Let A be equal
to B ...
Σελίδα 10
If the same is to be proved of the trebles , quadruples , & c . , then to each
magnitude are to be taken two , three , & c . magnitudes , equal to it . COR . 15. If
there be two unequal magnitudes , and from the double of the greater he taken
the ...
If the same is to be proved of the trebles , quadruples , & c . , then to each
magnitude are to be taken two , three , & c . magnitudes , equal to it . COR . 15. If
there be two unequal magnitudes , and from the double of the greater he taken
the ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD added alternate angle ABC angle BAC applied aret assigned axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line succession surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Σελίδα 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Σελίδα 72 - Any two sides of a triangle are together greater than the third side.
Σελίδα 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Σελίδα 103 - ... twice as many right angles as the figure has sides.
Σελίδα 70 - Any two angles of a triangle are together less than two right angles.
Σελίδα 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Σελίδα 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |
| Συγγραφέας | Thomas Perronet Thompson |
| Έκδοση | 4 |
| Εκδότης | Robert Heward, 1833 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 26 Απρ. 2007 |
| Μέγεθος | 150 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |