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 26.
Σελίδα 30
... consequently is not represented . ] The surfaces of the spheres shall coincide no where but in CD . For if this be disputed , First Case ; let it be assumed that they coincide in a belt of surface having breadth , as that contained ...
... consequently is not represented . ] The surfaces of the spheres shall coincide no where but in CD . For if this be disputed , First Case ; let it be assumed that they coincide in a belt of surface having breadth , as that contained ...
Σελίδα 33
... consequently the spheres INTERC . 4. are ‡ without change of place ; and if these spheres are supposed imbedded in one inclosed body of hard matter which is turned * INTERC . 9. along with them round * the straight line AC , this ...
... consequently the spheres INTERC . 4. are ‡ without change of place ; and if these spheres are supposed imbedded in one inclosed body of hard matter which is turned * INTERC . 9. along with them round * the straight line AC , this ...
Σελίδα 38
... consequently their point of contact C will occupy the same place as before , and their intersection will coincide with their intersection before the transposition , and , like it , will be without change of place during any turning of ...
... consequently their point of contact C will occupy the same place as before , and their intersection will coincide with their intersection before the transposition , and , like it , will be without change of place during any turning of ...
Σελίδα 41
... consequently the turning might be con- tinued till the point B coincided with A , every point in the straight line MQ remaining without change of place ; whence , if in MQ had been taken any point as R , and RA and RB had been joined ...
... consequently the turning might be con- tinued till the point B coincided with A , every point in the straight line MQ remaining without change of place ; whence , if in MQ had been taken any point as R , and RA and RB had been joined ...
Σελίδα 45
... consequently the planes will coincide throughout the straight lines which form the sides of such figure . But if the planes do not also coincide in all that is within the figure , then from two points [ among the points in which the ...
... consequently the planes will coincide throughout the straight lines which form the sides of such figure . But if the planes do not also coincide in all that is within the figure , then from two points [ among the points in which the ...
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.