The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Resultat 1-5 av 26
Side 23
... reason , 2 . than BAC ; The exterior angle CEB of the triangle ABE is greater and it has been demonstrated that the angle BDC is greater than CEB ; much more then 3. The angle BDC is greater than the angle BAC . Therefore , if from the ...
... reason , 2 . than BAC ; The exterior angle CEB of the triangle ABE is greater and it has been demonstrated that the angle BDC is greater than CEB ; much more then 3. The angle BDC is greater than the angle BAC . Therefore , if from the ...
Side 35
... reason , EF is equal to BC ; wherefore ( Ax . 1. ) 1. AD is equal to EF ; and DE is common ; therefore ( Ax . 2. or 3. ) 2. The whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to ...
... reason , EF is equal to BC ; wherefore ( Ax . 1. ) 1. AD is equal to EF ; and DE is common ; therefore ( Ax . 2. or 3. ) 2. The whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to ...
Side 36
... reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . — THEOREM . Triangles upon the same base and between the ...
... reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . — THEOREM . Triangles upon the same base and between the ...
Side 40
... reason , 3. The triangle KGC is equal to the triangle KFC . Then because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; ( Ax . 2. ) 4. The triangle AEK together with the triangle KGC is equal to the ...
... reason , 3. The triangle KGC is equal to the triangle KFC . Then because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; ( Ax . 2. ) 4. The triangle AEK together with the triangle KGC is equal to the ...
Side 44
... reason 2. AB and AH are in the same straight line . And because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and ( Ax . 2. ) 3. The whole angle DBA is equal to the whole FBC ...
... reason 2. AB and AH are in the same straight line . And because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and ( Ax . 2. ) 3. The whole angle DBA is equal to the whole FBC ...
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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Uten tilgangsbegrensning - 1854 |
The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Euclid,Samuel A. GOOD Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
Populære avsnitt
Side 26 - 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. either the sides adjacent to the equal...
Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Side 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.
Side 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Side 97 - 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 of the line which touches it.
Side 7 - AB; but things which are equal to the same are equal to one another...
Side 14 - To 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 intotwo equal parts.
Side 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.
Side 41 - 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.
Side 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced...