## A Supplement to the Elements of Euclid |

### Inni boken

Resultat 1-5 av 29

Side 12

Theorem . Any one side of a

remaining sides . Let ABCD be a given

, as BC , is less than the aggregate of the remaining sides . For , first , let the

figure ...

Theorem . Any one side of a

**rectilineal figure**is less than the aggregate of theremaining sides . Let ABCD be a given

**rectilineal figure**: Any D E F B C one side, as BC , is less than the aggregate of the remaining sides . For , first , let the

figure ...

Side 29

1. ) ; but ( constr . ) the LEAG = LD ; .. LAGC = LD . PROP . XXVI . 36. THEOREM .

If all the angles but one of any

angles but one , of another

1. ) ; but ( constr . ) the LEAG = LD ; .. LAGC = LD . PROP . XXVI . 36. THEOREM .

If all the angles but one of any

**rectilineal figure**, be together , equal to all theangles but one , of another

**rectilineal figure**having the ELEMENTS OF EUCLID . Side 30

angles but one , of another

the remaining angle of the one figure , shall be equal to the remaining angle of

the other : And , conversely , if an angle in the one figure be equal to an angle in

the ...

angles but one , of another

**rectilineal figure**having the same number of sides ,the remaining angle of the one figure , shall be equal to the remaining angle of

the other : And , conversely , if an angle in the one figure be equal to an angle in

the ...

Side 53

The diameters of an equilateral four - sided plane

another at right angles . Let AB and DC be the diameters of the equilateral four -

sided figure ACBD , cutting one an . other in E : AB and DC bisect one another in

E ...

The diameters of an equilateral four - sided plane

**rectilineal figure**bisect oneanother at right angles . Let AB and DC be the diameters of the equilateral four -

sided figure ACBD , cutting one an . other in E : AB and DC bisect one another in

E ...

Side 67

For , produce FA , so that it shall meet BC in I , and HG in K ; produce , also , GC

and HB , until they meet EP and DQ in L and M ; .. the

; and , since ( constr . ) ... A plane

For , produce FA , so that it shall meet BC in I , and HG in K ; produce , also , GC

and HB , until they meet EP and DQ in L and M ; .. the

**figures**FACL , FABM are D; and , since ( constr . ) ... A plane

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### Vanlige uttrykk og setninger

ABCD aggregate arch base bisect centre chord circle ABC circumference common constr construction describe a circle describe the circle diameter difference distance divided double draw E equal equiangular equilateral extremities fall figure finite straight line four fourth given circle given finite straight given point given ratio given rectilineal given square given straight line greater half inscribed isosceles join less Let ABC lines be drawn locus magnitudes manifest manner mean meet opposite sides parallel to BC parallelogram pass perimeter perpendicular polygon PROBLEM produced PROP proportional proposition rectangle contained rectilineal figure right angles right L scribed segment semi-diameter shewn sides similar square taken tangent THEOREM third touch the circle trapezium triangle vertex vertical whole

### Populære avsnitt

Side 310 - 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.

Side 198 - 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, together with the square...

Side 366 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...

Side 92 - If there be 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.

Side 284 - And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth...

Side 349 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.

Side 288 - Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth.

Side 296 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...

Side 367 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 104 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...