The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |
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Página 20
... common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB ; and the triangle AFC to the triangle F AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to ...
... common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB ; and the triangle AFC to the triangle F AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to ...
Página 21
... common to the two triangles BFC , CGB ; wherefore the triangles are equalb and their remaining angles , each to each , to which the equal sides are opposite ; F therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
... common to the two triangles BFC , CGB ; wherefore the triangles are equalb and their remaining angles , each to each , to which the equal sides are opposite ; F therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
Página 22
... common to both , D the two sides , DB , BC are equal to the two AC , CB , cach to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
... common to both , D the two sides , DB , BC are equal to the two AC , CB , cach to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
Página 27
... common to the two triangles DAF , EAF ; the two sides DA AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; с therefore the angle DAF is equal to the angle EAF : wherefore the given ...
... common to the two triangles DAF , EAF ; the two sides DA AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; с therefore the angle DAF is equal to the angle EAF : wherefore the given ...
Página 28
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; A с therefore the base AD is equal to the base © DB , and the straight line AB is divided ...
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; A с therefore the base AD is equal to the base © DB , and the straight line AB is divided ...
Otras ediciones - Ver todas
The First Two Books of the Elements of Euclid, with Additional Figures ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angled triangle angles CBA angles equal Arithmetic base BC BC is equal bisected BOOK bound centre cloth coincide Delectus diameter double English Notes equal to BC equal to twice Eton Eton College Euclid's Elements Exercises exterior angle four right angles Geography given point given rectilineal angle given straight line gnomon greater Greek half a right interior and opposite isosceles JANE MARCET join Let ABC Let the straight Lexicon M.A. New Edition Maps opposite angle parallel to CD parallelogram perpendicular Post 8vo produced Proposition rectangle BC rectangle contained rectilineal figure remaining angle rhombus right angles Schools Shrewsbury School sides BA sides equal square described square of AC THEOR triangle ABC twice the rectangle VALPY Valpy's wherefore xxxi
Pasajes populares
Página 18 - If two triangles have two sides of the one equal to two sides of the...
Página 67 - 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.
Página 51 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 109 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.
Página 12 - Mrs. R. Lee's Elements of Natural History ; or, First Principles of Zoology : Comprising the Principles of Classification, interspersed with amusing and instructive Accounts of the most remarkable Animals.
Página 53 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Página 76 - 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.
Página 34 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the same straight line with it but BD, which therefore is in the same straight line with CB.
Página 11 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 37 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.