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 74.
Σελίδα 15
... common to the two tri- angles FAC , GAB ; therefore these two triangles have the two sides FA , AC respectively equal to the two sides GA , AB , and the included angle FAC equal to the in- cluded angle GAB . Therefore they are equal in ...
... common to the two tri- angles FAC , GAB ; therefore these two triangles have the two sides FA , AC respectively equal to the two sides GA , AB , and the included angle FAC equal to the in- cluded angle GAB . Therefore they are equal in ...
Σελίδα 17
... common to the two triangles DBC , ACB , and the angles ABC , ACB equal by hyps ; therefore these two triangles have the two sides DB , BC respectively equal to the two sides AC , CB , and the included angle DBC equal to the in- cluded ...
... common to the two triangles DBC , ACB , and the angles ABC , ACB equal by hyps ; therefore these two triangles have the two sides DB , BC respectively equal to the two sides AC , CB , and the included angle DBC equal to the in- cluded ...
Σελίδα 21
... common to the two triangles ADF , AEF ; therefore these two triangles have the three sides AD , DF , FA of the one respectively equal to the three sides AE , EF , FA of the other . Therefore they are equal in every respect ( i . 8 ) ...
... common to the two triangles ADF , AEF ; therefore these two triangles have the three sides AD , DF , FA of the one respectively equal to the three sides AE , EF , FA of the other . Therefore they are equal in every respect ( i . 8 ) ...
Σελίδα 22
... common to the two triangles FDC , FEC : there- fore these two triangles have the three sides FD , DC , CF respectively equal to the three sides FE , EC , CF. fore they are equal in every respect ( i . 8 ) ; and hence the angle DCF is ...
... common to the two triangles FDC , FEC : there- fore these two triangles have the three sides FD , DC , CF respectively equal to the three sides FE , EC , CF. fore they are equal in every respect ( i . 8 ) ; and hence the angle DCF is ...
Σελίδα 23
Euclides Henry Judge Hose. COR . - Two straight lines cannot have a part common to both , or a common segment . pos- For if they can ; let , if sible , the two straight lines ABC , ABD have the part AB common to both , or the com- mon ...
Euclides Henry Judge Hose. COR . - Two straight lines cannot have a part common to both , or a common segment . pos- For if they can ; let , if sible , the two straight lines ABC , ABD have the part AB common to both , or the com- mon ...
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.