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
A sphere may be turned in any manner whatsoever about its centre , without
change of place . ... they touch only in a point ; and if they are turned as one body
about the two centres which remain at rest , the point of contact remains unmoved
.
A sphere may be turned in any manner whatsoever about its centre , without
change of place . ... they touch only in a point ; and if they are turned as one body
about the two centres which remain at rest , the point of contact remains unmoved
.
Σελίδα 14
Spheres described about the same centre , are called concentric . CoR . 2. A
sphere may be described about any centre , and with a central distance equal to
the distance of any two points that shall have been assigned . For it may be done
as ...
Spheres described about the same centre , are called concentric . CoR . 2. A
sphere may be described about any centre , and with a central distance equal to
the distance of any two points that shall have been assigned . For it may be done
as ...
Σελίδα 15
If the centres of two spheres coincide , and their central distances are equal ; their
surfaces will coincide throughout . And if their central distances are not equal ,
their surfaces will not coincide at all , but one be interior to the other . For ( by Cor
...
If the centres of two spheres coincide , and their central distances are equal ; their
surfaces will coincide throughout . And if their central distances are not equal ,
their surfaces will not coincide at all , but one be interior to the other . For ( by Cor
...
Σελίδα 17
1 either or both of the spheres may be turned in any manner whatsoever about its
centre , and they must still always coincide in the surface in fixed space CEGDHF
and not elsewhere . For each of them will be * without change of place ...
1 either or both of the spheres may be turned in any manner whatsoever about its
centre , and they must still always coincide in the surface in fixed space CEGDHF
and not elsewhere . For each of them will be * without change of place ...
Σελίδα 18
But if So , it may be shown as before , that they must continue to coincide in the
same line in fixed space CEGDHF and not elsewhere , in whatsoever manner
they may be turned about their respective centres . Let then the sphere whose
centre ...
But if So , it may be shown as before , that they must continue to coincide in the
same line in fixed space CEGDHF and not elsewhere , in whatsoever manner
they may be turned about their respective centres . Let then the sphere whose
centre ...
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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 |