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 21.
Σελίδα 56
If two triangles have two sides of the one , equal to two sides of the other
respectively ; and have also the angles belween those sides , equal to one
another ; they ... AB to DE , and AC to DF ; F and the angle ' BAC equal to the
angle EDF .
If two triangles have two sides of the one , equal to two sides of the other
respectively ; and have also the angles belween those sides , equal to one
another ; they ... AB to DE , and AC to DF ; F and the angle ' BAC equal to the
angle EDF .
Σελίδα 57
In any isoskeles triangle , the angles opposite to two equal sides are equal to one
another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC .
The angles ACB and ABC shall be equal to one another . * INTERC.12 .
In any isoskeles triangle , the angles opposite to two equal sides are equal to one
another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC .
The angles ACB and ABC shall be equal to one another . * INTERC.12 .
Σελίδα 58
If two angles of a triangle are equal to one another , the sides opposite to the two
equal angles are equal to one another . Let BAC be a triangle having the angle
ACB D. equal to the angle ABC ; the side BA is equal to the side CA. For if BA be
...
If two angles of a triangle are equal to one another , the sides opposite to the two
equal angles are equal to one another . Let BAC be a triangle having the angle
ACB D. equal to the angle ABC ; the side BA is equal to the side CA. For if BA be
...
Σελίδα 61
Let BAC , EDF be two triangles , A DG having the two sides BA , AC , equal to the
two sides DE , DF respectively , viz . ... The angle BAC shall be equal to the angle
EDF ; and the triangle BAC to the triangle EDF ; and the other angles , to which ...
Let BAC , EDF be two triangles , A DG having the two sides BA , AC , equal to the
two sides DE , DF respectively , viz . ... The angle BAC shall be equal to the angle
EDF ; and the triangle BAC to the triangle EDF ; and the other angles , to which ...
Σελίδα 68
To bisect a given angle . [ That is , to divide it into two equal angles . ] Let BAC be
the given angle . It is required to bisect it . First Case ; if BAC is less than the sum
of two right angles . Take any point D in AB , and from 1.3 . AC cut off * AE equal ...
To bisect a given angle . [ That is , to divide it into two equal angles . ] Let BAC be
the given angle . It is required to bisect it . First Case ; if BAC is less than the sum
of two right angles . Take any point D in AB , and from 1.3 . AC cut off * AE equal ...
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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 |