The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |
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Σελίδα 59
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD shall be equal to the parallelogram EBCF . CASE I. If the sides AD , DF of the parallelograms DBCF , ABCD , opposite to the base BC ...
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD shall be equal to the parallelogram EBCF . CASE I. If the sides AD , DF of the parallelograms DBCF , ABCD , opposite to the base BC ...
Σελίδα 60
Euclides Nicholas Pocock. BOOK I. then , because ABCD is a parallelogram , AD is equal a to BC : a 6 Ax . b 1 Ax . c 2 ... ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q.E.D. PROP . XXXVI ...
Euclides Nicholas Pocock. BOOK I. then , because ABCD is a parallelogram , AD is equal a to BC : a 6 Ax . b 1 Ax . c 2 ... ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q.E.D. PROP . XXXVI ...
Σελίδα 61
... ABCD , EFGH be parallelograms upon equal bases BC , FG , and between the same parallels AH , BG ; the parallelogram ABCD is equal to EFGH . Join BE , CH ; B A E And because BC is equal to FG , and FG to a EH , BC is equal to EH ; F G ...
... ABCD , EFGH be parallelograms upon equal bases BC , FG , and between the same parallels AH , BG ; the parallelogram ABCD is equal to EFGH . Join BE , CH ; B A E And because BC is equal to FG , and FG to a EH , BC is equal to EH ; F G ...
Σελίδα 66
... ABCD is double of the triangle ABC , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. BOOK I. PROP . XLII . PROB . To describe ...
... ABCD is double of the triangle ABC , because the diameter AC divides it into two equal parts ; wherefore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. BOOK I. PROP . XLII . PROB . To describe ...
Σελίδα 68
... ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is through which AC passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore called ...
... ABCD be a parallelogram , of which the diameter is AC , and EH , FG the parallelograms about AC , that is through which AC passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore called ...
Άλλες εκδόσεις - Προβολή όλων
The First Two Books of the Elements of Euclid, with Additional Figures ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 11 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.