The first two books of the Elements of Euclid, with additional figures, notes, explanations, and deductions, by N. Pocock1852 |
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Σελίδα 20
... THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an Isosceles triangle , of which the side AB ...
... THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an Isosceles triangle , of which the side AB ...
Σελίδα 22
... THEOR . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the ...
... THEOR . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the ...
Σελίδα 23
Euclides Nicholas Pocock. BOOK I. PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and ...
Euclides Nicholas Pocock. BOOK I. PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and ...
Σελίδα 24
... triangle is upon a side of the other , is shown in the annexed figure ; where it is manifest that , A D B whether CA be equal to DA or not , CB cannot be equal to DB . ] PROP . VIII . THEOR . If two triangles have 24 THE ELEMENTS.
... triangle is upon a side of the other , is shown in the annexed figure ; where it is manifest that , A D B whether CA be equal to DA or not , CB cannot be equal to DB . ] PROP . VIII . THEOR . If two triangles have 24 THE ELEMENTS.
Σελίδα 25
Euclides Nicholas Pocock. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one ...
Euclides Nicholas Pocock. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one ...
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.