Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
Im Buch
Ergebnisse 1-5 von 10
Seite 10
... ancient philosophers devoted much attention : this formed their sublime geometry , and their most strenuous efforts were put forth in its successful prosecution . Such were the principal subjects of speculation which en- gaged the ...
... ancient philosophers devoted much attention : this formed their sublime geometry , and their most strenuous efforts were put forth in its successful prosecution . Such were the principal subjects of speculation which en- gaged the ...
Seite 11
... ancient geometers . Plato himself was both a distinguished philosopher and an ingenious geometrician , as his invention of the geometrical analysis fully proves , who by his instructions and example created and cherished in the minds of ...
... ancient geometers . Plato himself was both a distinguished philosopher and an ingenious geometrician , as his invention of the geometrical analysis fully proves , who by his instructions and example created and cherished in the minds of ...
Seite 12
... ancients regarded the properties of these beautiful curves as objects merely of interesting speculation , in the detection of which they exercised their mental powers , but they never applied them to any practical purpose . In modern ...
... ancients regarded the properties of these beautiful curves as objects merely of interesting speculation , in the detection of which they exercised their mental powers , but they never applied them to any practical purpose . In modern ...
Seite 13
... ancients found it necessary to introduce a new method of demonstration , that of exhaustions , the most subtile and in ... ancient times , employed the method of exhaustions with admirable address in establishing most of his discoveries ...
... ancients found it necessary to introduce a new method of demonstration , that of exhaustions , the most subtile and in ... ancient times , employed the method of exhaustions with admirable address in establishing most of his discoveries ...
Seite 14
... ancients employed the principle of supraposition , or mentally applying one of the magnitudes to the other , and by a process of reasoning evincing their equality or inequality . To this was added the method of proportion , which may in ...
... ancients employed the principle of supraposition , or mentally applying one of the magnitudes to the other , and by a process of reasoning evincing their equality or inequality . To this was added the method of proportion , which may in ...
Andere Ausgaben - Alle anzeigen
Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Keine Leseprobe verfügbar - 2008 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 46 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Seite 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Seite 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.