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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Σελίδα 2
... produced ever so far both ways , do not meet . 12. A figure is that which is enclosed by one or more boundaries . 13. Rectilineal figures are those which are contained by straight lines : * Thus , if ABC , DBC could both be straight ...
... produced ever so far both ways , do not meet . 12. A figure is that which is enclosed by one or more boundaries . 13. Rectilineal figures are those which are contained by straight lines : * Thus , if ABC , DBC could both be straight ...
Σελίδα 5
... simplicity and distinctness . To join two points is an abbreviated expression , meaning the same as to draw a straight line from one of them to the other . 2. That a terminated straight line may be produced to Book 1. ] 5 OF EUCLID .
... simplicity and distinctness . To join two points is an abbreviated expression , meaning the same as to draw a straight line from one of them to the other . 2. That a terminated straight line may be produced to Book 1. ] 5 OF EUCLID .
Σελίδα 6
... produced to any length in a straight line : 3. That a circle may be described from any centre , at any dis- tance from that centre . * AXIOMS . 1. Things which are equal to the same , or to equals , are equal to one another . 2. If ...
... produced to any length in a straight line : 3. That a circle may be described from any centre , at any dis- tance from that centre . * AXIOMS . 1. Things which are equal to the same , or to equals , are equal to one another . 2. If ...
Σελίδα 7
... produced . * PROPOSITION I. PROBLEM . + To describe an equilateral triangle on a given finite straight line . ‡ Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . Let AB be perpendicular to ...
... produced . * PROPOSITION I. PROBLEM . + To describe an equilateral triangle on a given finite straight line . ‡ Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . Let AB be perpendicular to ...
Σελίδα 10
... produced , till it and the part added would be equal to AB . PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; † and have also the angles contained by those sides equal to ...
... produced , till it and the part added would be equal to AB . PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; † and have also the angles contained by those sides equal to ...
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 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...