The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 σελίδες |
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Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 15
... bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is re- quired to bisect it . A Take any point D in AB , and from AC cut off * AE * 3. 1 . equal to AD ; join ...
... bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is re- quired to bisect it . A Take any point D in AB , and from AC cut off * AE * 3. 1 . equal to AD ; join ...
Σελίδα 16
... bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . * Describe upon it an equilateral triangle ABC , and bisect the ...
... bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . * Describe upon it an equilateral triangle ABC , and bisect the ...
Σελίδα 18
... bisect * FG in H , and join CH ; the straight line CH , drawn from the given point C , shall be perpendicular to the given straight line AB . * 8. 1 . Join CF , CG , and because FH is equal to HG , and HC common to the two triangles FHC ...
... bisect * FG in H , and join CH ; the straight line CH , drawn from the given point C , shall be perpendicular to the given straight line AB . * 8. 1 . Join CF , CG , and because FH is equal to HG , and HC common to the two triangles FHC ...
Σελίδα 21
... Bisect AC in E , join BE and in BE produced make EF equal to BE , and join FC . Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , because they are ...
... Bisect AC in E , join BE and in BE produced make EF equal to BE , and join FC . Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , because they are ...
Σελίδα 36
... bisects them , that is , divides them into two equal parts . N. B. A parallelogram is a four - sided figure , of which ... bisect it . Because AB is parallel to CD , A and BC meets them , the alter- nate angles ABC , BCD are * * 29. 1 ...
... bisects them , that is , divides them into two equal parts . N. B. A parallelogram is a four - sided figure , of which ... bisect it . Because AB is parallel to CD , A and BC meets them , the alter- nate angles ABC , BCD are * * 29. 1 ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 173 - 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 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Σελίδα 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 23 - Any two sides of a triangle are together greater than the third side.
Σελίδα 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Σελίδα 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Σελίδα 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.