Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 14
... whole structure of plane geometry rests . In comparing magnitudes one with another the ancients employed the principle of supraposition , or mentally applying one of the magnitudes to the other , and by a process of reasoning evincing ...
... whole structure of plane geometry rests . In comparing magnitudes one with another the ancients employed the principle of supraposition , or mentally applying one of the magnitudes to the other , and by a process of reasoning evincing ...
Σελίδα 22
... whole performance . Its position also , at the very commencement of the study , is peculiarly unfortunate . The fifth and seventh propositions in particular have always presented a formidable obstacle to beginners , and have tended ...
... whole performance . Its position also , at the very commencement of the study , is peculiarly unfortunate . The fifth and seventh propositions in particular have always presented a formidable obstacle to beginners , and have tended ...
Σελίδα 30
... whole of the one shall coincide with the whole of the other . 7. A SOLID is that which has length , breadth , and thickness . Cor . The extremities of a solid are surfaces . 8. A PLANE RECTILINEAL ANGLE is the opening between two ...
... whole of the one shall coincide with the whole of the other . 7. A SOLID is that which has length , breadth , and thickness . Cor . The extremities of a solid are surfaces . 8. A PLANE RECTILINEAL ANGLE is the opening between two ...
Σελίδα 33
... whole of one with the whole of the other , or exactly fill the same space , are said to be equal in every respect . 38. When the several parts of one magnitude can be made to coincide with those of another , the magnitudes are equal ...
... whole of one with the whole of the other , or exactly fill the same space , are said to be equal in every respect . 38. When the several parts of one magnitude can be made to coincide with those of another , the magnitudes are equal ...
Σελίδα 34
... whole is greater than its part . 9. The whole is equal to all its parts taken together . When in a construction , or in the course of a demonstration , a reference is made to a definition , a postulate 34 ELEMENTS OF PLANE GEOMETRY .
... whole is greater than its part . 9. The whole is equal to all its parts taken together . When in a construction , or in the course of a demonstration , a reference is made to a definition , a postulate 34 ELEMENTS OF PLANE GEOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2008 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal ABC and DEF ABC is equal acute adjacent angles ancient geometers angle ACD angle AGH angle BAC angles ABC angles equal angular magnitude base BC bisect centre circumference coincide diagonal drawn EBCF equal alternate angles equal Def equal to BC Euclid EUCLID'S ELEMENTS exterior angle figure has sides four right angles geometers given point given straight line greater than AC included angle interior opposite angle intersect isosceles triangle join less Let ABC Let the straight method method of exhaustions parallel lines parallel to CD parallelogram ABCD perpendicular PLANE GEOMETRY point F PROB proof properties of parallel PROPOSITION Pythagoras radius rectangle rectilineal figure reductio ad absurdum Scholium side AB side AC straight line BC THEOR theorem three angles three sides triangle ABC triangle DEF triangles are equal truths unequal vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Σελίδα 46 - Any two angles of a triangle are together less than two right angles.
Σελίδα 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Σελίδα 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Σελίδα 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Σελίδα 68 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Σελίδα 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Σελίδα 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.