Elementary geometry |
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Página 7
... fall on that other part . Def . 6. A plane surface , or plane , is a surface in which any two points being taken the straight line that joins them lies wholly in that surface . Def . 7. A plane figure is a portion of BOOK I. ...
... fall on that other part . Def . 6. A plane surface , or plane , is a surface in which any two points being taken the straight line that joins them lies wholly in that surface . Def . 7. A plane figure is a portion of BOOK I. ...
Página 13
... fall along the line RQ ; ( Ax . 2. ) therefore the angle DBC coincides with , and is equal to , the angle QRS . ( Ax . I. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves ...
... fall along the line RQ ; ( Ax . 2. ) therefore the angle DBC coincides with , and is equal to , the angle QRS . ( Ax . I. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves ...
Página 21
... fall on F. And because the angle B = the angle E , ( Hyp . ) therefore the line BA would fall along the line ED . And because the angle C = the angle F , ( Hyp . ) therefore the line CA would fall along the line FD : therefore the point ...
... fall on F. And because the angle B = the angle E , ( Hyp . ) therefore the line BA would fall along the line ED . And because the angle C = the angle F , ( Hyp . ) therefore the line CA would fall along the line FD : therefore the point ...
Página 22
... fall where C was . And because the angle C = the angle B , ( Hyp . ) the line CA would lie along BA , and BA along CA ; therefore the point A would coincide with its former posi- tion , and the lines AC , AB would coincide with the ...
... fall where C was . And because the angle C = the angle B , ( Hyp . ) the line CA would lie along BA , and BA along CA ; therefore the point A would coincide with its former posi- tion , and the lines AC , AB would coincide with the ...
Página 27
... fall on the point E ; ( Hyp . ) and because the angle BAC is greater than the angle EDF , the line AC will fall outside DF , as DG ; and BC will fall as EG . ( Hyp . ) Let DH be the bisector of the angle FDG , ( Ax . 4. ) meeting EG in ...
... fall on the point E ; ( Hyp . ) and because the angle BAC is greater than the angle EDF , the line AC will fall outside DF , as DG ; and BC will fall as EG . ( Hyp . ) Let DH be the bisector of the angle FDG , ( Ax . 4. ) meeting EG in ...
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Términos y frases comunes
ABCD angle ABC angle APB angle BAC base bisect bisector Book called centre chord circle circumference coincide College common Constr construct converse Crown 8vo diagonals diameter difference distance divided double draw Edition ELEMENTARY equal angles Euclid Examples exterior angle extremities fall figure Find follows four Geometry given angle given point given straight line greater half Hence Illustrations included inscribed interior intersect isosceles triangle Join length less Let ABC line drawn locus magnitudes measure meet middle point minor arc opposite sides parallel parallelogram pass perpendicular placed polygon PROBLEM produced Professor Proof proportional quadrilateral radius ratio rectangle contained rectilineal figure regular required to prove respectively right angles School segment Shew sides similar Similarly square supplementary tangent THEOREM third touch triangle ABC unequal
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