A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Resultat 1-5 av 44
Side 19
... BC is equal to BA . [ Def . 15. ] But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB . But things which are equal to the same thing are equal to one another ; [ Ax . 1. ] therefore CA is equal ...
... BC is equal to BA . [ Def . 15. ] But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB . But things which are equal to the same thing are equal to one another ; [ Ax . 1. ] therefore CA is equal ...
Side 20
... equal to a given straight line . 1 . Let A be the given point , and BC the given straight line . It is required to draw from the point A a straight line equal to BC . 2 . From the point A to B draw the straight line AB ; [ Post . 1 ...
... equal to a given straight line . 1 . Let A be the given point , and BC the given straight line . It is required to draw from the point A a straight line equal to BC . 2 . From the point A to B draw the straight line AB ; [ Post . 1 ...
Side 22
... equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one ... BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each ...
... equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one ... BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each ...
Side 23
... BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10. ] Therefore the base BC coincides with the base EF , and is equal to it . [ Ax . 8. ] Therefore the whole triangle ABC ...
... BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Ax . 10. ] Therefore the base BC coincides with the base EF , and is equal to it . [ Ax . 8. ] Therefore the whole triangle ABC ...
Side 25
... equal to AF , show that the angles ABC and ACB are equal to one another . 2. The opposite angles of a rhombus are ... BC is common to both , the two sides DB , BC are equal to the two sides 3 . AC , CB , each to each ; and the BOOK I. 6 . 25.
... equal to AF , show that the angles ABC and ACB are equal to one another . 2. The opposite angles of a rhombus are ... BC is common to both , the two sides DB , BC are equal to the two sides 3 . AC , CB , each to each ; and the BOOK I. 6 . 25.
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.