Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Side 5
... long before they were collected and arranged in any regular order . The progress also of different nations in the path of geometrical discovery would A probably be very unequal , and would correspond to the PREFACE. ...
... long before they were collected and arranged in any regular order . The progress also of different nations in the path of geometrical discovery would A probably be very unequal , and would correspond to the PREFACE. ...
Side 6
Euclides. probably be very unequal , and would correspond to the urgency of the motives which impelled them to prosecute the study and to their views of its practical importance in promoting those arts which ameliorate and embellish ...
Euclides. probably be very unequal , and would correspond to the urgency of the motives which impelled them to prosecute the study and to their views of its practical importance in promoting those arts which ameliorate and embellish ...
Side 27
... unequal , and if unequal , one of them must be greater than the other . AB is then supposed to be greater than AC , and a part BD is cut off from AB , and supposed equal to AC ; and DC being joined , it is demonstrated , by means of the ...
... unequal , and if unequal , one of them must be greater than the other . AB is then supposed to be greater than AC , and a part BD is cut off from AB , and supposed equal to AC ; and DC being joined , it is demonstrated , by means of the ...
Side 31
... unequal . 20. A RIGHT - ANGLED triangle is that which has a right angle . The side opposite to the right angle is called the hypotenuse . 21. An OBTUSE - ANGLED triangle is that which has an obtuse angle . 22. An ACUTE - ANGLED triangle ...
... unequal . 20. A RIGHT - ANGLED triangle is that which has a right angle . The side opposite to the right angle is called the hypotenuse . 21. An OBTUSE - ANGLED triangle is that which has an obtuse angle . 22. An ACUTE - ANGLED triangle ...
Side 33
... unequal . A PROPOSITION is a distinct portion of abstract science , the verbal statement of which is called its enunciation , and is either a theorem or a problem . A THEOREM is a proposition which requires to be established by a ...
... unequal . A PROPOSITION is a distinct portion of abstract science , the verbal statement of which is called its enunciation , and is either a theorem or a problem . A THEOREM is a proposition which requires to be established by a ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Ingen forhåndsvisning tilgjengelig - 2008 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 46 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Side 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Side 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.