The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Βιβλίο 11853 |
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Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 62
... square on AB . From A draw ( i . 11 ) AC at right angles to AB ; and from ac cut off ( i . 3 ) AD equal to AB . Through D draw ( i . 31 ) DE parallel to AB ; and through B draw BF parallel to ac , cutting DE in F. Then ABFD shall be the ...
... square on AB . From A draw ( i . 11 ) AC at right angles to AB ; and from ac cut off ( i . 3 ) AD equal to AB . Through D draw ( i . 31 ) DE parallel to AB ; and through B draw BF parallel to ac , cutting DE in F. Then ABFD shall be the ...
Σελίδα 63
... square are parallels . PROP . XLVII . THEOR . In any right - angled triangle the square , which is de- scribed on ... AC , including the right angle . On BC , AB , AC describe ( i . 46 ) the three squares BDEC , BFGA , AHKC ; through a ...
... square are parallels . PROP . XLVII . THEOR . In any right - angled triangle the square , which is de- scribed on ... AC , including the right angle . On BC , AB , AC describe ( i . 46 ) the three squares BDEC , BFGA , AHKC ; through a ...
Σελίδα 64
... AL ; there- fore the parallelogram BL is double ( i . 41 ) of the tri- angle ABD . And because the square GB and the tri- angle CFB are on the same base FB and between the same parallels FB , GAC ; therefore the square GB is double of ...
... AL ; there- fore the parallelogram BL is double ( i . 41 ) of the tri- angle ABD . And because the square GB and the tri- angle CFB are on the same base FB and between the same parallels FB , GAC ; therefore the square GB is double of ...
Σελίδα 65
... squares of EA , AC are equal ( Ax . 2 ) to the squares of BA , AC . But the square of EC is equal ( i . 47 ) to the squares of EA , AC , because the angle CAE is a right angle by const " ; and the square of BC is equal to the squares of BA ...
... squares of EA , AC are equal ( Ax . 2 ) to the squares of BA , AC . But the square of EC is equal ( i . 47 ) to the squares of EA , AC , because the angle CAE is a right angle by const " ; and the square of BC is equal to the squares of BA ...
Σελίδα 69
... AC shall be equal to the square of AB . On AB describe ( i . 46 ) the square ADEB ; and through c draw ( i . 31 ) CF parallel to AD or BE , cutting DE in F. A с B D F E The figures AF , CE are parallelograms by const " ; and since each ...
... AC shall be equal to the square of AB . On AB describe ( i . 46 ) the square ADEB ; and through c draw ( i . 31 ) CF parallel to AD or BE , cutting DE in F. A с B D F E The figures AF , CE are parallelograms by const " ; and since each ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Δημοφιλή αποσπάσματα
Σελίδα 39 - 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...
Σελίδα 52 - 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 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Σελίδα 11 - 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 likewise those which are terminated in the other extremity.
Σελίδα 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 66 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Σελίδα 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.