A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Side vi
... called an ' abstract science . ' A further point to be noticed in regard to the definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the groundwork of the entire ...
... called an ' abstract science . ' A further point to be noticed in regard to the definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the groundwork of the entire ...
Side ix
... called the general enunciation of the proposition , after which comes the discussion . First , the general enunciation is repeated and applied to a particular figure . By this means the attention is limited to a special instance ...
... called the general enunciation of the proposition , after which comes the discussion . First , the general enunciation is repeated and applied to a particular figure . By this means the attention is limited to a special instance ...
Side x
... called a syllogism , i.e. , an argument stated at length , and in such a form as to show the truth of the reasoning in the most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as ...
... called a syllogism , i.e. , an argument stated at length , and in such a form as to show the truth of the reasoning in the most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as ...
Side xi
... called the premisses , and the last the conclusion ; and it will be noticed that the principle which underlies and justifies the reasoning is this , that whatever is true of an entire class must be true of every member of that class ...
... called the premisses , and the last the conclusion ; and it will be noticed that the principle which underlies and justifies the reasoning is this , that whatever is true of an entire class must be true of every member of that class ...
Side 14
... called a right angle ; and the straight line which stands on the other is called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13 ...
... called a right angle ; and the straight line which stands on the other is called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13 ...
Andre utgaver - Vis alle
A School Euclid. Being Books I. & II. of Euclid's Elements, with Notes ... Euclid,Charles Mansford Uten tilgangsbegrensning - 1875 |
A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ... Euclides Uten tilgangsbegrensning - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle DBA angle EDF angle equal angles are equal axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid EUCLID'S ELEMENTS exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal
Populære avsnitt
Side 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Side 28 - If two triangles have two sides of the one equal to two sides of the...
Side 41 - Any two sides of a triangle are together greater than the third side.
Side 57 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Side 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Side 75 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Side 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Side 69 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.