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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Αποτελέσματα 1 - 5 από τα 25.
Σελίδα 26
... called a radius of the sphere . A straight line drawn through the centre and
terminated both ways by the surface , is called a diameter of the sphere . Cor . A
straight line may be described or made to pass from any one point to any other
point .
... called a radius of the sphere . A straight line drawn through the centre and
terminated both ways by the surface , is called a diameter of the sphere . Cor . A
straight line may be described or made to pass from any one point to any other
point .
Σελίδα 27
All the radii of the same or equal spheres are equal . And spheres that have ...
And if two spheres have equal radii , the extremities of the radii ( by Cor . 3 above
) are ... The sphere that has the greater radius , is the greater . For if ( See the ...
All the radii of the same or equal spheres are equal . And spheres that have ...
And if two spheres have equal radii , the extremities of the radii ( by Cor . 3 above
) are ... The sphere that has the greater radius , is the greater . For if ( See the ...
Σελίδα 28
Therefore the concentric sphere that cuts AB in any point that is between B and A
( that is to say , which has a radius less than AB ) is less than the sphere whose
radius is AB ; or the sphere whose radius is AB , is the greater . Cor . 6. A sphere
...
Therefore the concentric sphere that cuts AB in any point that is between B and A
( that is to say , which has a radius less than AB ) is less than the sphere whose
radius is AB ; or the sphere whose radius is AB , is the greater . Cor . 6. A sphere
...
Σελίδα 30
Let now the sphere whose centre is B , be turned about the point G , till its centre
B is applied to the centre A of the other sphere ( which can be * INTERC.10 .
done inasmuch as the radii of these equal spheres are * Cor . 4 . + INTERC .
Let now the sphere whose centre is B , be turned about the point G , till its centre
B is applied to the centre A of the other sphere ( which can be * INTERC.10 .
done inasmuch as the radii of these equal spheres are * Cor . 4 . + INTERC .
Σελίδα 33
About B as a centre , with the radii BC and BD * Interc.10 . respectively , describe
* concentric spheres . ... and about B as a centre , with the radius BE , describe a
sphere , whose surface ( because it lies within the surfaces which pass through ...
About B as a centre , with the radii BC and BD * Interc.10 . respectively , describe
* concentric spheres . ... and about B as a centre , with the radius BE , describe a
sphere , whose surface ( because it lies within the surfaces which pass through ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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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 |