inroad

Etymology

The noun is derived from in + road (“(obsolete) act of riding on horseback; hostile ride against a particular area, raid”). The verb is derived from the noun.

noun

1. (military, also figurative) An advance into enemy territory, an attempted invasion; an encroachment, an incursion.
   […] That ſince that time he Archibald Douglas, 6th Earl of Angus] was become the ſubject of King Henry [VIII] of England, his Majeſty's James V of Scotland's] greateſt enemy; and was now the cauſe of all the Inroads made by the English into Scotland: […] 1537, David Scott, “Papers Illustrative of the Trial of Jonet Lady Glammys. I. Narrative Taken from the History of Scotland, by David Scott of the Inner Temple.”, in Robert Pitcairn, compiler], Criminal Trials and Other Proceedings before the High Court of Justiciary in Scotland, part IX (Trials during the Reigns of King James the Fourth and Fifth), [Edinburgh]: Printed at the Bannatyne Club Press by Ballantyne and Co., published 1831, →OCLC, page 192
   [A] child knowing the heate of fire, will as readely iudge of the perrill, as the wiſeſt Senatour, of the inroad of a borderer, or the politick captaine, of the vnequall encoũter with his enimy, […] 1586, T[imothie] Bright, “The Particular Aunswere to the Obiections Made in the II Chapter”, in A Treatise of Melancholie.[…], London: […] Thomas Vautrollier,[…], →OCLC, page 75
   Whence is it that ſo many corrupt Opinions have made ſuch an Inroad on Proteſtant Religion, and the Profeſſion of it? Is it not from hence, that many have loſt an Experience of the power and efficacy of the Truth, and ſo have parted with it? 1683, Samuel Annesley, “The Chamber of Imagery in the Church of Rome Laid Open; or An Antidote against Popery. […] Sermon X.”, in A Continuation of Morning-Exercise Questions and Cases of Conscience, Practically Resolved by Sundry Ministers, in October, 1682, London: […] J. A. for John Dunton[…], →OCLC, page 221
   [T]he discourse of ornament was energetically appropriated by those anxious to defend masculinity and protect feminine virtue against the inroads of luxury and its ill effects on morality. 2009, Marcia Pointon, “Fault Lines and Points of Light”, in Brilliant Effects: A Cultural History of Gem Stones and Jewellery, New Haven, Conn., London: […] [F]or the Paul Mellon Centre for Studies in British Art by Yale University Press, part 1 (Stories Touching Stones), page 19, column 1
   [I]n many European states, the whole notion of retirement at pensionable age and consequential entitlement to a pension seems to fall within the domain of social security law rather than forming part of the contract-based system of regulation of termination of employment. There may therefore be significant inroads into the notion of a unified or integrated contract-based system of regulation of termination of employment. However, in most European legal systems it would seem that these inroads do not encroach upon the essential integrity or unity of the contract-based system of regulation of termination of employment. 2011, Mark Freedland, Nicola Kountouris, “The Termination and Transformation of Employment Contracts”, in The Legal Construction of Personal Work Relations, Oxford, Oxfordshire: Oxford University Press, page 224
2. (figurative, usually in the plural) Often followed by in, into, or on: initial progress made toward accomplishing a goal or solving a problem.
   Three weeks into it, I am finally beginning to make inroads on this project.
   You must have been fairly surprised at Dr. Glaser's inroads into reprogramming the brain. 10 October 1983, Eugenie Ross-Leming, Brad Buckner, “If Thoughts Could Kill”, in Scarecrow and Mrs. King, season 1, episode 3
   Even in our post-Darwinian society, with evolutionary theory making inroads in many areas of the social and human sciences, the cynics' insight retains an ability to stimulate and to provoke. 2005, Yiannis Gabriel, “Foreword”, in Ian Cutler, Cynicism from Diogenes to Dilbert, Jefferson, N.C., London: McFarland & Company, pages 2–3
   These insights open up novel inroads in the area of neurorehabilitation by demonstrating that disorders such as amblyopia might be accessible to perceptual training protocols. 2014, Mark W. Greenlee, “The Neuronal Base of Perceptual Learning and Skill Acquisition”, in Stephen Billett, Christian Harteis, Hans Gruber, editors, International Handbook of Research in Professional and Practice-based Learning (Springer International Handbooks of Education), Dordrecht: Springer, →DOI, →ISSN, part II (Research Paradigms), page 330

verb

1. (intransitive, archaic) To make advances or incursions.
   [Y]ou muſt not expect him to go with you, inroading or making incurſions into Georgia; for he is an Armenian, true to his faith; and not a Georgian, falſe and diſtruſtful! 1792, Joseph Emin, The Life and Adventures of Joseph Émïn, an Armenian.[…], London: s.n.], →OCLC, page 358
   All about the dreaming sea-board, but tucked well out of sight, lurked those guardians of the environment—filters, slurpers, booms, vacuums, ultramodern aids to deal with the very latest imperishables. All ruinously expensive to mount, and inroading sizeably into profit margins, but part of the small print that nearly drove Boyle barmy. 1982, Kamala Markandaya [pseudonym; Kamala Purnaiya], chapter 26, in Shalimar (A Cornelia & Michael Bessie Book), 1st U.S. edition, New York, N.Y., Cambridge, Cambridgeshire: Harper & Row, page 167
   […] Kvenland and Scythian Amazons […] poisoned Anund and his troops when they were inroading in Vinland or Kvenland. 2018, Pia Piiroinen, Me Habirut Mahabharata: Part 1, Helsinki, Finland, Norderstedt, Schleswig-Holstein, Germany: Books on Demand, page 147
2. (transitive, obsolete) To make an inroad into (something).
   The kyngdom of Heven be Chriſt, 'teys reſembled to this noble kyng / With riches inroded mercy for to lern, and to have compaſſion. / One of another, after goddes Faſſyon. 1781, “Hundred of Depwade”, in History and Antiquities of the County of Norfolk, volumes II (Containing the Hundreds of Clavering, Depwade, Diss, and Earsham), Norwich, Norfolk: […] J. Crouse, for M. Booth,[…], →OCLC, footnote *, page 127
   Furthermore, what initially was the main domain of record labels—the financing of music productions—was also inroaded by business outsiders. 2012, Peter Tschmuck, “The Digital Music Revolution”, in Creativity and Innovation in the Music Industry, Heidelberg, Baden-Württemberg, New York, N.Y.: Springer, →DOI, page 194
   [I]n June 2008, the Ras Doumeirah incident happened. Eritrean forces inroaded the Ras Doumeirah principality, a strategic place at the narrowest crossing point to the Gulf of Aden at the strait of Babeal Mendeb. 2019, Everisto Benyera, “Borders and the Coloniality of Human Mobility: A View from Africa”, in Inocent Moyo, Christopher Changwe Nshimbi, editors, African Borders, Conflict, Regional and Continental Integration (Border Regions Series), Abingdon, Oxfordshire, New York, N.Y.: Routledge