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 10.
Σελίδα 62
To bisect a given straight line . ( That is , to divide it into two equal parts . ] G B В '
D Let AB be the given straight line . It is res quired to bisect it . * 1.1 . Describe ...
Join CF , and let CF cut AB in G. AB is bisected in G. + Constr . Because in the ...
To bisect a given straight line . ( That is , to divide it into two equal parts . ] G B В '
D Let AB be the given straight line . It is res quired to bisect it . * 1.1 . Describe ...
Join CF , and let CF cut AB in G. AB is bisected in G. + Constr . Because in the ...
Σελίδα 68
To bisect a given angle . ... Wherefore the given angle BAC is bisected by the
straight line AF . ... straight line , and DE be bisected by the point A , and AF be
perpendicular to BAC and bisect the angle BAC by dividing it into two right
angles .
To bisect a given angle . ... Wherefore the given angle BAC is bisected by the
straight line AF . ... straight line , and DE be bisected by the point A , and AF be
perpendicular to BAC and bisect the angle BAC by dividing it into two right
angles .
Σελίδα 70
In the same manner if the side BC be bisected , may be shown that the angle
BCG is greater than CBA . But the angle + J. 15 . BCG ist equal to ACD , for they
are vertical angles ; therefore Interc . 1. the angle ACD is alsof greater than CBA .
In the same manner if the side BC be bisected , may be shown that the angle
BCG is greater than CBA . But the angle + J. 15 . BCG ist equal to ACD , for they
are vertical angles ; therefore Interc . 1. the angle ACD is alsof greater than CBA .
Σελίδα 76
And because the angle CDF has been shown to be bisected by the straight line
DG , and * Constr . was also * bisected by the straight line DB , DG and DB aret in
+ I. 9. Cor . 11.13.Cor.2 . one straight line ; wherefore EB shall pass through G ...
And because the angle CDF has been shown to be bisected by the straight line
DG , and * Constr . was also * bisected by the straight line DB , DG and DB aret in
+ I. 9. Cor . 11.13.Cor.2 . one straight line ; wherefore EB shall pass through G ...
Σελίδα 85
7 . angle CED is bisected by the straight line EZ ; and because in the angles DEF
, CEF , the sides ED and EF are equal to the sides EC and EF respectively , and
the angle DEF has been shown to + 1. 4 . be equal to the angle CEF , FD ist ...
7 . angle CED is bisected by the straight line EZ ; and because in the angles DEF
, CEF , the sides ED and EF are equal to the sides EC and EF respectively , and
the angle DEF has been shown to + 1. 4 . be equal to the angle CEF , FD ist ...
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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 |