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 ix
The Axiom which declared the whole to be greater than its part , has been
omitted as amounting , after the explanation of the terms ' greater ' and ' less '
introduced from Euclid's Book of Data , to no more than the proposition that ' the
greatest ...
The Axiom which declared the whole to be greater than its part , has been
omitted as amounting , after the explanation of the terms ' greater ' and ' less '
introduced from Euclid's Book of Data , to no more than the proposition that ' the
greatest ...
Σελίδα 2
To which is Added an Appendix ... Thomas Perronet Thompson. See Note . See
Note . XV . A magnitude is said to be greater than another by a certain magnitude
, when this last - mentioned magnitude being taken from the first , the remainder ...
To which is Added an Appendix ... Thomas Perronet Thompson. See Note . See
Note . XV . A magnitude is said to be greater than another by a certain magnitude
, when this last - mentioned magnitude being taken from the first , the remainder ...
Σελίδα 5
For example , if the original proposition is , that if of equals one be greater than
some thing else , the rest are severally greater than the same ; the negative of
this proposition is , that if of equals one be not greater than some thing ...
For example , if the original proposition is , that if of equals one be greater than
some thing else , the rest are severally greater than the same ; the negative of
this proposition is , that if of equals one be not greater than some thing ...
Σελίδα 6
If of equals , one be greater , or less , than some thing else ; the rest are severally
greater , or less , than the same . Or if some thing be greater , or less , than one ; it
is greater , or less , than each of the others also . Let A and B be equal , and let ...
If of equals , one be greater , or less , than some thing else ; the rest are severally
greater , or less , than the same . Or if some thing be greater , or less , than one ; it
is greater , or less , than each of the others also . Let A and B be equal , and let ...
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 ...
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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 |