Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Σελίδα 15
... conclusions . Prosecuting the study of the science . on this principle alone , the ancient geometers by their success- ful efforts widely extended its domain , and brought it to such a state of perfection as to prepare it for the ...
... conclusions . Prosecuting the study of the science . on this principle alone , the ancient geometers by their success- ful efforts widely extended its domain , and brought it to such a state of perfection as to prepare it for the ...
Σελίδα 20
... conclusion might be arrived at with perfect accuracy . A line might be drawn from the vertex of any triangle to the base , and by a very simple application of this principle the vertex of the triangle might be conceived to move along ...
... conclusion might be arrived at with perfect accuracy . A line might be drawn from the vertex of any triangle to the base , and by a very simple application of this principle the vertex of the triangle might be conceived to move along ...
Σελίδα 21
... conclusions , and obviating difficulties which admit of no other mode of solution . It might also prove very useful to students to have some acquaintance with the nature and use of variation before they advanced to that part of mathe ...
... conclusions , and obviating difficulties which admit of no other mode of solution . It might also prove very useful to students to have some acquaintance with the nature and use of variation before they advanced to that part of mathe ...
Σελίδα 22
... conclusions . Almost the only exception to this is the assumption which he has made in his twelfth axiom , and which he was compelled to introduce in order to effectuate a demonstration of the pro- perties of parallel lines . It is ...
... conclusions . Almost the only exception to this is the assumption which he has made in his twelfth axiom , and which he was compelled to introduce in order to effectuate a demonstration of the pro- perties of parallel lines . It is ...
Σελίδα 24
... conclusions deduced from the suppositions and reasonings brought forward in the proof of a proposition . If the conclusions are in harmony with the axiom applicable to the particular case , they are received as veritable truths ; but if ...
... conclusions deduced from the suppositions and reasonings brought forward in the proof of a proposition . If the conclusions are in harmony with the axiom applicable to the particular case , they are received as veritable truths ; but if ...
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.