Volume 1

Lexicon technicum: or, an universal English dictionary of arts and sciences / [John Harris].

  • Harris, John, 1667?-1719
Date:
1736
Catalogue details

Licence: Public Domain Mark

Credit: Lexicon technicum: or, an universal English dictionary of arts and sciences / [John Harris]. Source: Wellcome Collection.

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    HYOTHYROIDES [of Coufu and du&ttits, Gr.] are two Mulcles of the Larynx, proceeding from the inferior Fart of the Bone Hyoides, la- „ terally artd oppolite to the Origination of the Ce- rat ogleffus. This pair of Mufcles defcends direftly to the lower part of the Cartilage Scutiformis : It Ufe is to draw the Larynx upwards in an acute Tone of the Voice ; the Canal of the Afpera At term being Sdfo fttaitned by it. HYPiETHRON, is an open Gallery or Build¬ ing, the inhde whereof is uncover’d, and exposed to the Weather. The Aiments gave this,Name .to all Temples which had no Roof; as that of Jupi¬ ter Otympius at Athens, having ten Columns in Front, as alfo two Rows in its exterior Sides, and one in the interior. • ... HYPALLAGE [t/'TaA\rf>n,Gr.^or Immntation, a Grammatical Figure, when of different Exprel- fions, which give the fame Idea, we make choice of that which is leaft ufed; or when there is a mutual Permutation or Change of Cafes: As in this Infiance, Dare Claffbus Aufiros, in Read of Dare Gaffes Auftris. HYPERBaTON [of vant&duvu, Gr. to tran- fcend,] a Grammatical Figure, where there is too bold and frequent a Tranfpoiition of Words. HYPERBOLA [i5tsp/?oAh, Gr.] in Geometry, is a Seftion of a Cone made by a Plane, fo that the Axis of the Seftion inclines to the oppolite Leg of the Cone, which in the Parabola is parallel to it, and in the Elhplis interfedls it. The Axis of the Hyperbolical Seftion will meet alfo with the op- polite fide of the Cone, when produced above the Vertex. Thus, in the annexed Figure, the Curve G E HF is an Hyperbola. Where the Line E D, being the Continuation of the Axis till it meet with the oppolite Cone, or oppolite lide of the former Cone C B produced, is called by the Name of the Latus Tr anfverfum and the middle Point of that Line E D, is called the Centre of the Seftion, or rather of the cppofite Sedions. PROP. L In an Hyperbola GEHF, the Square of the Ordi- nate I K, is equal both to the Red angle L I, made under the Parameter L E, and the Abfciffa E 1; and alfo to the Reftangle L S, made under the Ablcilfa £ 1, (or L R) and another Line S R, which is a fourth Proportional to D E the Latus Tranlverfum, E L the Parameter, (or Latus Reft urn) and El the Able ilia. Let the lide of the Cone A B, in which the Se- ftion is, be called a ; and thro’ B the Vertex of the Cone, draw B M parallel to the Axis of the Sefti- on, and which call b. Let the intercepted part of , , t » * »• V the Diameter of the Bale A M be called c. Let E / e b. Then by comparing the limilar Tri¬ angles ABM and E l N, 1N, in this way of Notation, will be e c. And if you put M C £± d, and the Tianlverfe Diameter D E — o b; then will D I =r. o b -f e b. And by realon of the Similarity of the Triangles B MC, D E P, and D 10, you will find that E P mult be exprdled by o d, and I 0 by o d -f- e d, and conlequently, — e d. (The General Reafon of all which way of Notation, and the way of working to ob¬ tain it, you will fee in the Parabola.) This done, ’tis plain that K I Square mull betrr to the Reftangle N10 ; that is, in this Notati- o e c d -f e e c d, as you will find by Multi- on plication. Wherefore, if o e c d -f e e c d, the Square of IK, bedividedby the Abfciffa EI~ebj the Quotient mull be fuch a Line, which, together with E I, can make a Reftangle equal to the Square of / K: Wherefore the Reftangle E S zzz IK Square, which in this Notation will be o e c d + e e c or contraftedly, o c d y e c d e b This done, proceed (as direfted in Cor. i. Prop. i. of the Parabola, to find the Latus Re Gum) by faying^ As b : c :: o d: ~in Words, As the Pa¬ rallel to theSeftion : is to the part of the Diameter of the Bale intercepted :: So is the Latus Prima- rium : to a fourth Proportional ; ’tis plain* the fourth Term will be one part of the Line IS, or ° -y- — Latus ReGum R 1 (or other will be found thus: m this Notation L E.) And b Celled: the c e d ~T~ • As Or, according to Apollonius's way of Expreffion in this Propolition : As o b : —~ :: e b : t~~ * for that will be found to be the fourth Proporti¬ onal as before : Which is now found out according the Terms of the Propolition, between the Latus Tr anfverfum o b, and the Latus ReGum , and the Abfciffa e b. Wherefore oecd + eecd, the Square of the Ordinate / K, is mamfelily equal to the Reftan¬ gle under the Latus ReGum and the Abfciffa ; and alfo to another under the Abfciffa, and the fourth Proportional., Q. E. D. COROL*