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 ...Robert Heward, 1833 - 150 σελίδες |
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Αποτελέσματα 6 - 10 από τα 21.
Σελίδα 41
... radius AR , will + INTERC.10 . bet greater than the sphere described about the same centre with Cor . 5. the radius AC ; and its surface will not coincide at all with the surface of the other , but be exterior ; for if it coincided at ...
... radius AR , will + INTERC.10 . bet greater than the sphere described about the same centre with Cor . 5. the radius AC ; and its surface will not coincide at all with the surface of the other , but be exterior ; for if it coincided at ...
Σελίδα 42
... radius AN + INTERC.10 . will be less than the sphere with the radius AM , and its surface INTERC . 3. will be interior to the surface of the other throughout , and in the Cor . 4 . Cor . 5 . Cor . 4 . same manner the surface of the ...
... radius AN + INTERC.10 . will be less than the sphere with the radius AM , and its surface INTERC . 3. will be interior to the surface of the other throughout , and in the Cor . 4 . Cor . 5 . Cor . 4 . same manner the surface of the ...
Σελίδα 43
... radius of the circle ; and any straight line drawn through the centre and terminated both ways by the circumference , is called a diameter of the circle . B When a circle is said to be described about the centre A with the radius AB ...
... radius of the circle ; and any straight line drawn through the centre and terminated both ways by the circumference , is called a diameter of the circle . B When a circle is said to be described about the centre A with the radius AB ...
Σελίδα 44
... radius . For a plane of unlimited extent ( as by Cor . 1 above ) may be made to pass through the proposed centre , and turned till it also pass through the other extremity of the proposed radius ; by the revo- lution of the radius in ...
... radius . For a plane of unlimited extent ( as by Cor . 1 above ) may be made to pass through the proposed centre , and turned till it also pass through the other extremity of the proposed radius ; by the revo- lution of the radius in ...
Σελίδα 49
... radius AB , the meaning is , that it is described by the revolution of the given straight line AB about the extremity A. A circle may be described about any centre and with any radius . All the radii of the same circle are equal . And ...
... radius AB , the meaning is , that it is described by the revolution of the given straight line AB about the extremity A. A circle may be described about any centre and with any radius . All the radii of the same circle are equal . And ...
Άλλες εκδόσεις - Προβολή όλων
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 adjacent angles alternate angles angle ABC angle ACB angle BAC angular points assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater half the angle hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore
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.