The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 14
... join DC . Then because in the tri- angles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and ( hyp . ) the angle DBC is equal to the angle ACB ; therefore ...
... join DC . Then because in the tri- angles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and ( hyp . ) the angle DBC is equal to the angle ACB ; therefore ...
Σελίδα 16
... join DE , and upon it de- scribe ( I. 1. ) an equilateral triangle DEF , on the side remote from A ; † then join AF : AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides ...
... join DE , and upon it de- scribe ( I. 1. ) an equilateral triangle DEF , on the side remote from A ; † then join AF : AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides ...
Σελίδα 17
... join BG and CF , and the straight line joining their point of intersec- tion with A bisects the angle . The proof , which is easy , is left to exercise the learner . † This problem is a particular case of the ninth proposition of the ...
... join BG and CF , and the straight line joining their point of intersec- tion with A bisects the angle . The proof , which is easy , is left to exercise the learner . † This problem is a particular case of the ninth proposition of the ...
Σελίδα 18
... join FC ; FC is the required line . * F AD CEB Because DC is equal to CE , and FC common to the two tri- angles DCF ... join CG ; the straight line CG is the perpendicular required . † Join CE , CF. Then because EG is equal to GF ...
... join FC ; FC is the required line . * F AD CEB Because DC is equal to CE , and FC common to the two tri- angles DCF ... join CG ; the straight line CG is the perpendicular required . † Join CE , CF. Then because EG is equal to GF ...
Σελίδα 22
... joining C with the extremity of the produced part . The following proof is very neat and easy : From AC cut off AD equal to AB ; bisect ( 1.9 . ) the angle BAC by the straight line AE , and join ED . Then in the triangles BAE , DAE , BA ...
... joining C with the extremity of the produced part . The following proof is very neat and easy : From AC cut off AD equal to AB ; bisect ( 1.9 . ) the angle BAC by the straight line AE , and join ED . Then in the triangles BAE , DAE , BA ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - 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 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...