The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Libro 11853 |
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Resultados 1-5 de 31
Página 10
... exterior angles ; ( 2 ) the angles AFG , FGC , DGF , GFB , are called interior angles ; ( 3 ) any angle at F is said to be opposite to any angle at G ; ( 4 ) the interior angles which are opposite to one another , and on different sides ...
... exterior angles ; ( 2 ) the angles AFG , FGC , DGF , GFB , are called interior angles ; ( 3 ) any angle at F is said to be opposite to any angle at G ; ( 4 ) the interior angles which are opposite to one another , and on different sides ...
Página 28
... exterior angle shall be greater than either of the in- terior and opposite angles . Let ABC be a triangle , and let one of its sides BC be produced to D. Then the exterior angle ACD shall be greater than either of the two interior and ...
... exterior angle shall be greater than either of the in- terior and opposite angles . Let ABC be a triangle , and let one of its sides BC be produced to D. Then the exterior angle ACD shall be greater than either of the two interior and ...
Página 29
... angle AKB is B equal to the angle мKC , since they are opposite vertical angles ( i . 15 ) : therefore the two ... exterior angle ACD is greater than either of the two interior and opposite angles CAB , ABC . Which was to be proved ...
... angle AKB is B equal to the angle мKC , since they are opposite vertical angles ( i . 15 ) : therefore the two ... exterior angle ACD is greater than either of the two interior and opposite angles CAB , ABC . Which was to be proved ...
Página 30
... angle ABC shall be greater than the angle BCA . From AC , which is by hyp greater than AB , cut off ( i . 3 ) AD equal to AB ; and join BD . B A D C Because the side CD of the tri- angle BCD is produced to A , the exterior angle BDA is ...
... angle ABC shall be greater than the angle BCA . From AC , which is by hyp greater than AB , cut off ( i . 3 ) AD equal to AB ; and join BD . B A D C Because the side CD of the tri- angle BCD is produced to A , the exterior angle BDA is ...
Página 32
... angle BDC shall be greater than the angle BAC . Construct as before . Because the side ED of the triangle CDE is produced to B , the exterior angle BDC is greater ( i . 16 ) than the interior and opposite angle CED . And be- cause the ...
... angle BDC shall be greater than the angle BAC . Construct as before . Because the side ED of the triangle CDE is produced to B , the exterior angle BDC is greater ( i . 16 ) than the interior and opposite angle CED . And be- cause the ...
Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.