A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 29
Euclides Charles Mansford. if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will ...
Euclides Charles Mansford. if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will ...
Página 36
... BC , BD , on the opposite sides of AB , make the adjacent angles ABC , ABD together equal to two right angles : BD shall be in the same straight line with CB . 2 . For if BD be notin the same straight line with CB , let BE be in the ...
... BC , BD , on the opposite sides of AB , make the adjacent angles ABC , ABD together equal to two right angles : BD shall be in the same straight line with CB . 2 . For if BD be notin the same straight line with CB , let BE be in the ...
Página 38
... BC be bisected , and the side AC be produced to G , it may be proved that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15. ] Therefore , if one side , & c . Q.E.D. Ex . Construct the figure mentioned at ...
... BC be bisected , and the side AC be produced to G , it may be proved that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15. ] Therefore , if one side , & c . Q.E.D. Ex . Construct the figure mentioned at ...
Página 39
... BC . 2. Only one perpendicular can be drawn from the same point to the same straight line . 3. The equal angles of an isosceles triangle must be both acute . PROPOSITION 18. THEOREM . The greater side of every triangle is opposite to ...
... BC . 2. Only one perpendicular can be drawn from the same point to the same straight line . 3. The equal angles of an isosceles triangle must be both acute . PROPOSITION 18. THEOREM . The greater side of every triangle is opposite to ...
Página 41
... sides of it are to- gether greater than the third side ; name- ly , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . 2 . Produce BA to the point D , making AD equal to AC [ I. 3 ] , and join DC ...
... sides of it are to- gether greater than the third side ; name- ly , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . 2 . Produce BA to the point D , making AD equal to AC [ I. 3 ] , and join DC ...
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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