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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Σελίδα xii
... consequently , has length and breadth , but not thickness . For if it had thickness , it would not be the boundary , but part of the solid . VI . That which bounds a surface , is called a line . VII . A line , consequently , has length ...
... consequently , has length and breadth , but not thickness . For if it had thickness , it would not be the boundary , but part of the solid . VI . That which bounds a surface , is called a line . VII . A line , consequently , has length ...
Σελίδα 11
... consequently ( by Cor . 16 ) the magnitudes would not be all equal to one another . Which cannot be , for they are equal . The assumption + therefore cannot be true ; or there is not a magnitude which they cannot pass . That is , they ...
... consequently ( by Cor . 16 ) the magnitudes would not be all equal to one another . Which cannot be , for they are equal . The assumption + therefore cannot be true ; or there is not a magnitude which they cannot pass . That is , they ...
Σελίδα 14
... consequently each point in the surface 1.Nom.11 . and B , are equally distant with A and B , or all the points in * 1.Nom.12 . the surface are equidistant * from B. Which was to be done . And by parity of reasoning , the like may be ...
... consequently each point in the surface 1.Nom.11 . and B , are equally distant with A and B , or all the points in * 1.Nom.12 . the surface are equidistant * from B. Which was to be done . And by parity of reasoning , the like may be ...
Σελίδα 27
... consequently is a * straight line . Nom . COR . 3. The straight lines between equidistant points , are equal . And the extremities of equal straight lines are equidistant . + I.Nom . 12. For if the points are equidistantt , they can be ...
... consequently is a * straight line . Nom . COR . 3. The straight lines between equidistant points , are equal . And the extremities of equal straight lines are equidistant . + I.Nom . 12. For if the points are equidistantt , they can be ...
Σελίδα 29
... consequently † without change of place , the surfaces will at all times during the turning coincide in the whole of such figure or figures and not elsewhere . For if they did not , they would at one instant coincide in some point in ...
... consequently † without change of place , the surfaces will at all times during the turning coincide in the whole of such figure or figures and not elsewhere . For if they did not , they would at one instant coincide in some point in ...
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.