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 12.
Σελίδα 10
... geometers were confined to the properties of rectilineal figures , or rather to those of tri- angles , into which all rectilineal figures may be resolved . The circle probably engaged their attention only as a convenient instrument in ...
... geometers were confined to the properties of rectilineal figures , or rather to those of tri- angles , into which all rectilineal figures may be resolved . The circle probably engaged their attention only as a convenient instrument in ...
Σελίδα 11
... geometers during 200 years after its introduction into Greece . To the Pythagorean succeeded the Platonic school , the institution of which forms an epoch of great importance in the history of geometry . By the successful efforts and ...
... geometers during 200 years after its introduction into Greece . To the Pythagorean succeeded the Platonic school , the institution of which forms an epoch of great importance in the history of geometry . By the successful efforts and ...
Σελίδα 12
... Geometers next turned their attention to the determination of the lengths and areas of curves . The methods of demon- stration which they had hitherto employed were amply suf- ficient for the comparison of triangles or circles with each ...
... Geometers next turned their attention to the determination of the lengths and areas of curves . The methods of demon- stration which they had hitherto employed were amply suf- ficient for the comparison of triangles or circles with each ...
Σελίδα 15
... geometers , as already mentioned , made the principle of supraposition the foundation of all their geometri- cal demonstrations , and were thus able to rear the structure of the science on a secure and solid basis . They were careful to ...
... geometers , as already mentioned , made the principle of supraposition the foundation of all their geometri- cal demonstrations , and were thus able to rear the structure of the science on a secure and solid basis . They were careful to ...
Σελίδα 16
... geometry since the time of Euclid has - caused so much perplexity and annoyance to geometers as the subject of parallel lines . There is no great difficulty in demonstrating , that if two straight lines make equal alternate angles with ...
... geometry since the time of Euclid has - caused so much perplexity and annoyance to geometers as the subject of parallel lines . There is no great difficulty in demonstrating , that if two straight lines make equal alternate angles with ...
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
AC is equal acute alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid extended exterior angle extremities four right angles geometers geometry given point given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means measurement meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle problem produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AB side AC surfaces THEOR theorem thing third triangle ABC triangles are equal truths unequal vertex wherefore whole
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.