A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 30
... figure . If BA and AC were in one straight line the construction and proof would exactly correspond to prop . 11 , the reason of which is obvious . Ex . 1. If two isosceles triangles be described on opposite sides of the same base the ...
... figure . If BA and AC were in one straight line the construction and proof would exactly correspond to prop . 11 , the reason of which is obvious . Ex . 1. If two isosceles triangles be described on opposite sides of the same base the ...
Página 37
... figure is a right angle , all the angles at E are right angles . 2. Let the four angles at E , taken in order , be bisected by the four straight lines EG , EH , EK , and EL . Show , 1 . That GE and KE are in the same straight line , and ...
... figure is a right angle , all the angles at E are right angles . 2. Let the four angles at E , taken in order , be bisected by the four straight lines EG , EH , EK , and EL . Show , 1 . That GE and KE are in the same straight line , and ...
Página 38
... [ I. 15. ] Therefore , if one side , & c . Q.E.D. Ex . Construct the figure mentioned at the end of the proposition , and show that ACD is greater than ABC . PROPOSITION 17. THEOREM . Any two angles of a triangle 388 EUCLID'S ELEMENTS .
... [ I. 15. ] Therefore , if one side , & c . Q.E.D. Ex . Construct the figure mentioned at the end of the proposition , and show that ACD is greater than ABC . PROPOSITION 17. THEOREM . Any two angles of a triangle 388 EUCLID'S ELEMENTS .
Página 43
... figure is less than that of the outer figure . Ex . If O be a point within the triangle ABC , prove that the sum of AO , BO , and CO is less than the sum of the three sides of the triangle . PROPOSITION 22. PROBLEM . To make a triangle ...
... figure is less than that of the outer figure . Ex . If O be a point within the triangle ABC , prove that the sum of AO , BO , and CO is less than the sum of the three sides of the triangle . PROPOSITION 22. PROBLEM . To make a triangle ...
Página 47
... figure to the proposition the point G must lie in the circumference of a circle drawn from centre D , with radius DG , and as the angle EDG is greater than EDF , the point G must be above EF . Thus the two cases just mentioned have not ...
... figure to the proposition the point G must lie in the circumference of a circle drawn from centre D , with radius DG , and as the angle EDG is greater than EDF , the point G must be above EF . Thus the two cases just mentioned have not ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid 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 less 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