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 . Consequences deducible from this are , that if two spheres
touch one another externally , they touch only in a point ; and if they are turned as
one ...
A sphere may be turned in any manner whatsoever about its centre , without
change of place . Consequences deducible from this are , that if two spheres
touch one another externally , they touch only in a point ; and if they are turned as
one ...
Σελίδα x
connu à l'inconnu . The difference may at first sight appear to be not much ; but if
all men would agree to treat of nothing that had not previously been laid out for
naming after the manner of the anatomists , the consequences in the aggregate ...
connu à l'inconnu . The difference may at first sight appear to be not much ; but if
all men would agree to treat of nothing that had not previously been laid out for
naming after the manner of the anatomists , the consequences in the aggregate ...
Σελίδα xii
... or points , in any manner that can be shown to be practicable with ihe hard
body on which they are understood to be represented . Nevertheless the
application of one object to another will , when required , be imagined to take
place without ...
... or points , in any manner that can be shown to be practicable with ihe hard
body on which they are understood to be represented . Nevertheless the
application of one object to another will , when required , be imagined to take
place without ...
Σελίδα 1
And in like manner two lines or points may actually touch one another and
coincide . But besides this , there is an imaginary coincidence frequently
appealed to by geometers ; which is , when it can be shown that coincidence
would take place ...
And in like manner two lines or points may actually touch one another and
coincide . But besides this , there is an imaginary coincidence frequently
appealed to by geometers ; which is , when it can be shown that coincidence
would take place ...
Σελίδα 6
And because B is equal to C , in like manner would B and C. But because A and
B would each coincide with C ; if the boundaries of both could be applied to those
of C at once , A and B would coincide with one another ; wherefore A and + 1.
And because B is equal to C , in like manner would B and C. But because A and
B would each coincide with C ; if the boundaries of both could be applied to those
of C at once , A and B would coincide with one another ; wherefore A and + 1.
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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 |